[NEXT-GEN Version]
If you're updating the mod, make sure to reinstall both main and patch files

Verify your game's cache/files.

Make sure "user.settings", "dx12user.settings" and "input.settings" files in '..Users\%user%\Documents\The Witcher 3' folder aren't set to read-only. 

If you have any version of "Magic Spells for Signs and Weapons" installed, delete the dlcAdtomes folder from your 'The Witcher 3 Wild Hunt\dlc\' directory and the Modadtomes folder from your 'The Witcher 3 Wild Hunt\mods\' directory.

If you update from the 3.52-ng version, remove the 'modMagicSpellsRevamped_NGEN_mod' folder from your 'mods' folder!

0) DO NOT use any installation managers, it's reported that they might miss some files.
1) Download the main 'Magic Spells' file
2) Copy contents of the main file ('bin', 'dlc' and 'mods') folders into your 'The Witcher 3 Wild Hunt' main directory.
3) Open inputsett.txt file in the main file archive and follow its instructions.
3.a) Ignore additionalInput.txt file, if this is your first installation
4) Download the Next-Gen patch, copy its content (the 'bin' and 'mods' folder) into your 'The Witcher 3 Wild Hunt' main directory, replacing the files.
Vladimir UI users:

5) Open Script Merger, refresh and re-merge any conflicting files.
5.a) If you get  script compilation errors, ignore everything that starts with "Warning" and pay attention to "Errors" - most likely you missed something during the installation or installed your other mods incorrectly.
6) Navigate to 'The Witcher 3 Wild Hunt\bin\config\r4game\user_config_matrix\pc\', add the following line to the end of both 'dx11filelist.txt' and 'dx12filelist.txt' files:
modAMagicSpells.xml;
6.a) OR simply use this utility
7) Run the game, go to the settings for this mod and set all four entries to default.
8) Play.

Additional notes: 

• I noticed that the game might revert its settings after installing some mods, so if you see the "Game has been updated" notification or something like that upon the game launch, you need to adjust the mod's settings again (set everything to Default, at least) and check if the input.settings file still has the spells keys (if it hasn't, add the keys from the inputsett.txt file again).
• (Irrelevant for Vladimir UI users)I've added the option "Always select last highlighted radial menu item": the Next-Gen radial menu works a bit differently now - to choose an item you not only have to scroll through items for it, but also confirm that selection. This option will "force choose" the last spell item (and only the spell item) you've scrolled to. So, if you, for example, were scrolling through the spell items, choosing what you need, and then moved the cursor to choose some bomb or sign, the last chosen (scrolled) spell item will be registered as "equipped" and you'll be able to cast its spells. 
  

[OLD 1.31(2) Version]
Verify your game's cache/files.

Install the Mod limit fix. 

Make sure your "user.settings" and "input.settings" files in '..Users\%user%\Documents\The Witcher 3' folder aren't set to read-only.

If you have any version of "Magic Spells for Signs and Weapons" installed, delete the dlcAdtomes folder from your 'The Witcher 3 Wild Hunt\dlc\' directory and the Modadtomes folder from your 'The Witcher 3 Wild Hunt\mods\' directory. 

0) DO NOT use any installation managers, it's reported that they might miss some files.
1) Copy the 'bin', 'dlc' and 'mods' folders into your 'The Witcher 3 Wild Hunt' main directory.
2) Open Script Merger, refresh and re-merge any conflicting files.

• If you use the Ghost Mode (or some other mod) and have troubles with merging the "effectTypes.ws" file, be sure to choose code chunks from the both mods (press CTRL+2, then CTRL+3), when merger shows a merging window.
• If you use W3EE, install the original mod and the corresponding compability file, run Script Merger, merge "actor.ws", "hudModuleRadialMenu.ws", "ProjectileTrajectory.ws", "r4Player.ws" and "locomotionDirectController.ws" files (don't worry that should be an automerge), skip the rest. Make sure that the optional folder has the highest priority.
• Witcher 3 - Enhanced Edition - Lazarus Project isn't supported. 
  

2.b) If you get  script compilation errors, ignore everything that starts with "Warning" and pay attention to "Errors" - most likely you missed something during the installation or installed your other mods incorrectly.
3) Open inputsett.txt file and follow its instructions.
3.b) Ignore additionalInput.txt file, if this is your first installation
4) Run the game, go to the settings for this mod and set all four entries to default.
5) Play.

Refer to the video tutorial by eyeONE below (timestamp - 2:54), if you have troubles

Spell items can be bought from ofieri and novigradian merchants (the ofieri Runewright sells more items when his work station is upgraded)
Map of the Merchants:
OR 
by using the console command: ashenmage

OR 
they can be obtained after completing certain main and side quests (You need to install the optional file)
List of quests and rewards: 

 

To cast spells, equip them in your inventory and select them from the radial menu. 
The spells are bound to your signs, you can see what spells are available for each sign by opening the radial menu and pressing the X (by default) key.
To see an additional info about each spell, hold that X key and navigate through the radial menu.

Then, after you've chosen a sign with the spell you need, press the "Cast Spell" button (E by default).
Pocket spells are tapped.
Trophy spells are held down. 

Damage modifiers for each spell can be seen in the additional info in the radial menu after you hold the X button. Some spells don't have them, it means, that they either calculated purely by your sign intensity and an opponent's health, or they deal no damage.

Some spells (e.g. fireballs) require a targeted enemy, i.e. its health bar should be shown.

Rage management perk support:

• you can disable it in the mod's main settings if you don't want to use it
• if you use W3EE/Lazarus, that probably won't do good for you, so you need to disable that perk support in the mod's main settings
• doesn't work with the Magical Doll (Swordless Spells) and the Bow of Ardat
• you can set to always use adrenaline first to cast spells (even if there's enough stamina) in the mod's main settings
• the amount of adrenaline you need to cast spells depends on the required stamina you set in the mod's settings (e.g. 75% of the stamina bar = 0.75 adrenaline points)
  

Magical Doll:
gives a massive bonus of additional spellpower to all signs if it's equipped.
if you're in a combat and have the Magical Doll equipped in the slot, you can sheathe your sword and perform various magical light and heavy attacks depending on your currently chosen sign.

• if you don't want that mechanic, unequip the Magical Doll
• automatically disables auto weapon sheathing, if it's enabled in your game's settings, and enables it back after the fight is over or you draw your sword manually
• includes some new (for Geralt) animations from an ofiery mage
• every attack consumes various amount of stamina
• you can perform the attack only if an enemy is targeted, i.e. its health bar should be shown
• you can cancel the attacks by pressing dodge, roll or block keys
• pressing the block key creates a short round wave pushing enemies back
• this mechanic doesn't affect fistfight minigames and other mandatory fistfights
  

Tome of Carrying:
 - Yrden - spell of the Void Book. Allows you to create the custom book with the existing spells of your choosing. Please, read the notes and watch the turotial video below thoroughly:

• If you're playing the Next-Gen version, it has only one pocket slot, so in order to add a spell from another pocket item, you can choose and equip it in the radial menu instead of the Tome of Carrying
• You can have only one custom spell book, but you can rearrange the spells at any time (even if you manage to add another Void Book, it will have the same spells you've set originally)
• If you enable the spell tooltip in the radial menu, the spell memorizing tooltip will be gone, you have to enable it again by pressing the "Witcher Senses" button
• You can't add manual aiming spells (they will work anyway, if you have another quickslot and/or trophy items, which contain such spells, equipped)
• You can't add Swordless spells (they will work anyway, if you have the Spell Doll in your inventory)
• You can't add the spell of the Void Book
• You can add the Lukatiel Sword buff, which charges your sword, crossbow and Rend attacks, but you won't be able to cast the Sword spells like yrden/fire waves
• Once placed in the quickslot and chosen, the Void Book overrides the spells of other items, except for those mentioned above(unequip it or choose another quickslot spell item to cast the spells of other equipped items) 
• The Assassin and Vampire dodges and rolls will work if you have the appropriate trophy item equipped
• You MUST destroy the special place of power by using the Igni sign on it, when you're done
• Tutorial Video:
  Spoiler:  

  Show
  
  

 - Igni - creates a light source
 - Aard - the spell currently does nothing, it's reserved for the future update.
 - Other signs - increases Geralt's encumberance and underwater swimming speed and air.

Manuscript of Clear Horizon:

• Igni - imbues your sword with energy.
• Axii - turn your sword into a magical dark blade
• Aard - drags a target to your position, move forward while casting to transfer yourself to the target.
• Other signs - makes Geralt invisible for a short time. Gives instant kill chance, increases signs power, chance and damage of critical hits while you're invisible. After the attack with a sword or a sign you'll loose invisibility. Cannot be cast during fights.
  

Tome of Meteora:

• Igni - imbues your sword with fire.
• Other signs - summons fire meteors to a target's location, number of meteors and decreasing of damage you receive scale with your signs intensity
  

Tome of Cold stars:

• Igni - imbues your sword with frost.
• Other signs - summons ice meteors to a target's location, number of meteors and decreasing of damage you receive scale with your signs intensity.
  

Tome of White Sphere:

• Igni - encases your sword with ice. 
• Any sign - creates an ice blast on a target's location, decreasing of damage you receive scales with your signs intensity.
  

Tome of Fire Entity:

• Yrden - summons fire golem.
• Igni - creates a fire line towards an enemy.
• Axii - fires a fire granade.
• Aard - a round fire attack.
  

Tome of Ice Entity:

• Yrden - summons ice golem.
• Igni - creates an icy line towards an enemy.
• Axii - fires ice shards, which pierces targets, has a chance to disarm a human npc if a projectile hit the arm.
• Aard - a round frost attack.
  

Tome of Rock Watcher:

• Yrden - summons stone golem.
• Igni - creates a stone line towards an enemy.
• Axii - fires stone projectile, has a chance to disarm a human npc if a projectile hit the arm.
• Aard - a round stone attack.
  

Tome of BloodMoon:
 - Yrden - creates a special trap, which pulls targets to its position.
 - Igni - imbues your sword with the blood flame, can apply bleeding and restore your health at critical attacks.
 - Axii - a life draining attack, heals you, you must be close to an enemy.
 - Aard - restrains targets in front of you, inflicting a bleeding. Can't be used against Wraiths and flying targets.
 - Quen - if you're in a combat, transfers you behind the current target, otherwise turns you into the flying smoke:

• Hold the "Sprint" key to speed up
• Hold the "Jump" (Spacebar by default) key to increase the altitude (B/circle for the gamepads)
• Hold the "Sheathe Sword" (C by default) key to decrease the altitude (X/Square for the gamepads)
• You can also hold the "Radial Menu" key and use your mouse to change the altitude
• Use with caution before/during quests, as you may miss event trigger areas
• Tap the "Cast Spell" key (E by default) to cancel the spell, be sure to find a safe spot for landing
• if you have the BloodMoon tome equipped in the trophy slot (or this particular spell in the Custom Spell Book) you can turn into the Bloodmoon Smoke while jumping, falling or swimming by pressing the Cast Spell Key (E by default)
  

Modifies your dodge and roll.

Tome of the Great Swamp:

• Yrden - creates an area of a poisonous fire on the ground at the target's position.
• Quen - imbues your sword with poison.
• Igni - a stream of a poisonous fire. Hold the Cast key to initiate the cast, to cancel it tap the Cast key again or press attack, block or dodge keys.
• Axii - shoots a venom projectile. If you hit Elementa, Ogroids or Relicts, your sword damage against them will be increased by 5% (up to 40%).
• Aard - creates a long cone of a poisonous fire.
  

Tome of the Fire Gnosis:

• Yrden - creates an area of a fire on the ground at the target's position.
• Quen - summons magical butterflies.
• Igni - a fire stream. Hold the Cast key to initiate the cast, to cancel it tap the Cast key again or press attack, block or dodge keys. Has a chance to increase your sword damage against hit targets (except for Vampires and Specters) up to 40%.
• Axii - shoots a fireball.
• Aard - creates a long cone of fire.
  

Tome of Permafrost:

• Yrden - creates an area of a frost fire on the ground at the target's position.
• Quen - healing spell.
• Igni -  a stream of a condensed frost. Hold the Cast key to initiate the cast, to cancel it tap the Cast key again or press attack, block or dodge keys.
• Axii - shoots a frost spear.
• Aard - creates a long cone of frost.
  

Tome "Eye of the Storm":
 - Axii - piercing dash towards an enemy, requires a sword equipped in the hand
 - Aard - completely slows down your opponents.
 - Igni - turns your sword into two claws attached to the hands, allowing you to perform dual wield attacks:

• Whether Geralt performs attack towards the camera direction or towards an enemy (vanilla targeting) depends on the "Cast Sword Spells towards Camera" option
• Requires a sword equipped in the hand
• Once you've summoned the Claws, open the radial menu, tap the tooltip key (X by default) to learn about controls and special actions
• To dispel the Claws cast the spell again
• if you sheathe or switch your sword, the Claws will be dispelled
  

 - Other signs - slows down the time, increases your speed.
Modifies your Roll (only the Roll, the Dodge remains the same) - you can interrupt it by pressing Attack, Block or Cast Spell (E by default) keys.

Scroll of Beauty:
 - Yrden - creates an area which slows down the time and blocks some of monsters abilities.
 - Igni - throws the magical dagger, deals little damage, but inflicts bleeding or poisoning. Has a chance to disarm a human npc if a projectile hit the arm.
 - Quen - transfers you behind the current target (followed by the critical attack, if you have a sword equipped in the hand)
 - Aard - creates sand pillars under the targets around
 - Axii - turns your sword into the Bow:

• Requires a sword equipped in the hand
• You need to set the 'Ardat Bow' option entry in the mod's menu to default after the first time you've updated the mod
• Once you've summoned the bow, open the radial menu, tap the tooltip key (X by default) to learn about controls and hold that key navigating through signs to learn about arrow effects
• Parry with the bow deflects projectiles
• Every arrow requires different amount of stamina to shoot (can be adjusted in the mod's options), if you don't have enough stamina, simple (Axii) arrows will be applied
• Axii arrows have a chance to disarm a human npc if they hit the arm
• You can parry close-range attacks with the bow
• To dispel the bow press the "Heavy Attack" key
• You must dispel the bow before any interactions (horse mounting, meditation, looting, fast travelling etc)
• In some cases the bow might be automatically dispelled, that was made to prevent certain bugs
• Try not to shoot npcs
  

Tome of Transference:
 - Yrden - teleportation spell; use with caution during quests, as you may miss quest trigger areas.
 - Igni - a strike to each surrounding enemy, requires a sword equipped in the hand
 - Aard - teleports a target to your position when it's at a distance, or away from you if it's in front of you.
 - Quen - transfers you behind the current target.
 - Axii - turns your sword into a Spear, also allowing you to use a shield to block attacks:

• All the attacks are heavy, thrust attaks deal more damage
• Whether Geralt performs attack towards the camera direction or towards an enemy (vanilla targeting) depends on the "Cast Sword Spells towards Camera" option
• Requires a sword equipped in the hand
• Once you've summoned the Spear, open the radial menu, tap the tooltip key (X by default) to learn about controls and special actions and hold that key navigating through signs to learn about the Spear spells
• Parry with the Shield deflects projectiles
• To dispel the Spear and Shield cast the spell again
• If you sheathe or switch your sword, the Spear and Shield will be dispelled
• While this mechanic is active, certain mods which modify animations (e.g. SCAAR) won't work, until you dispell it
  

Tome of Assassins Bless:

• Yrden - creates a tornado, which chases a randomly-selected target.
• Quen - increases your sword attack's speed and range, chance and bonus damage of critical hits.
• Igni - slashing attack
• Axii - decreases an enemy's speed and attack power. You must be close to a target.
• Aard - attaches a chain to your sword, lasts for 2 minutes, the chain dissappears if you sheathe the sword. Open the radial menu, hold the tooltip key (X by default) to learn about its effects before and after applying the spell.
  

Modifies your dodge and roll.

Tome of Energy:

• Yrden - creates an area which gives you an energy form, charges your sword, decreases incoming damage, deflects projectiles and blocks some of monsters abilities. It interferes with other shield spells, including quen.
• Quen - magical shield, which decreases and reflects a part of the incoming damage, and deflects projectiles.
• Igni - a stream of energy. Hold the Cast key to initiate the cast, to cancel it tap the Cast key again or press attack, block or dodge keys.
• Axii - strikes your enemy with an energy, might affect other opponents around.
• Aard - creates a long cone of energy.
  

Tome of Quileg Pyromancy:

• Yrden - creates a special trap, which pulls targets to its position.
• Quen - magical shield, which decreases and reflects a part of the incoming damage, and deflects projectiles.
• Igni - a stream of a condensed fire. Hold the Cast key to initiate the cast, to cancel it tap the Cast key again or press attack, block or dodge keys.
• Axii - fires small meteors to the opponents around.
• Aard - creates a fire blast.
  

The Sword Ring:
Upon the first cast with any sign gives you a buff, which:

• increases your sword's damage, giving additional effects, depending on your currently chosen sign
• allows to cast spells from the sword and your crossbow (sword's visual FX and crossbow spells might be disabled in the mod's settings), depending on your currently chosen sign
• modifies your Rend's attacks
• if you have 2 adrenaline points, the sword attacks deal more damage with an additional visual effect
  

See the additional info about the Sword Spells in the radial menu.

Bracelet of the Grave Warden:

• Yrden - creates an area, which gives you a spectral form, charges your sword, decreases incoming damage and blocks some of monsters abilities. Additionally increases your sword damage against Vampires, Specters and Cursed.
• Quen - addles the mind of a randomly-selected opponent for a short time (the Caparison of Lament effect).
• Axii - a single target attack, works only against Specters, Vampires and Cursed, has a chance to instantly banish a wraith.
• Aard - creates a cone of magical flame.
  

Flower wreath of the Forest Witch:

• Yrden - summons a panther.
• Axii - creates giant roots, damaging enemies around.
• Aard - restrains targets in front of you. Can't be used against Wraiths and flying targets.
  

Amulet of the Black Fire:

• Yrden - creates an area of a magical fire on the ground at the target's position.
• Quen - magical shield, which decreases and reflects a part of the incoming damage, and deflects projectiles.
• Igni - a stream of a magical fire. Hold the Cast key to initiate the cast, to cancel it tap the Cast key again or press attack, block or dodge keys.
• Axii - shoots a magical fire projectile.
• Aard - creates a cone of magical fire.
  

Ring of Winter Souls:

• Yrden - creates a winter tornado, which pulls targets to its position.
• Quen - magical shield, which decreases and reflects a part of the incoming damage, and deflects projectiles.
• Igni - a stream of a winter fire. Hold the Cast key to initiate the cast, to cancel it tap the Cast key again or press attack, block or dodge keys.
• Axii - creates a cone of frost fire.
• Aard - creates a winter blast.
  

Grimoire of the Old Gods:

• Yrden - creates a thunderstorm.
• Quen - a series of quick uninterupptable attacks on an enemy, requires a sword equipped in the hand
• Igni - a stream of a magical fire. Hold the Cast key to initiate the cast, to cancel it tap the Cast key again or press attack, block or dodge keys. Has a chance to block monsters special abilities for some time.
• Axii - fires an electrical spear.
• Aard - creates an electrical blast.
  

Manual Spell Aiming:
if you have certain spell item equipped and chosen in your quickslot (see the list below), you can press and hold the "Use item" key (Middle Mouse by default) to start the aiming, to cast a spell press the "Abort action" key (Spacebar by default), which is also used to cancel crossbow and bombs actions, you can cycle available spells by pressing the "Cast Spell" key (E by default), and to cancel the aiming release the "Use item" key. 
In order to cast an aiming spell of a trophy item you need to have any spell item equipped and chosen in your quickslot.
Aiming Spells:

• Tome of Fire Gnosis - the fireball and the area of a fire 
• Tome of Permafrost - the frost spear and the area of the frost fire 
• Tome of the Great Swamp - the venom projectile and the area of the poisonous fire
• Amulet of the Black Fire - the magical fire projectile and the area of the magical fire
• Tome of Energy - an energy landmine
• Tome of Ice Entity - the ice spear
• Tome of Fire Entity - the fire granade
• Tome of Rock Watcher - the stone projectile
• Grimoire of the Old Gods - the electrical spear and a heavy energy projectile
• Ring of Winter Souls - a frost landmine and heavy frost projectile
• Tome of Quileg Pyromancy - a fire landmine and a fast fire projectile 
• Tome of Assassins Bless - magical bolts which can inflict poison or bleeding effects (you can fire several of them in a row) and a heavy sand projectile
• Tome of BloodMoon -  you can place up to four pillars, which allow you to corral up your opponents (active for 29 seconds)
• Tome of BloodMoon -  a special stream attack, drains life from an opponent and heals you, if you're close enough
  

Every landmine is active for 30 seconds.

You can disable the slow-mo in the mod's main settings.

 

The mod settings contains many damage modifiers (among other options), which you can change to your liking.

Spell damages are scaled with your signs intensity and Geralt's level to make them better balanced. The duration of the inflicted effects are manually adjusted.

You can also change stamina modifiers such as cost and delay!

Keep in mind, that different enemies have various resistances, so e.g. poison spells can deal more damage to humans and less to drowners.