With the author's notes in bold.

SPOILER ALERT

SPOILER ALERT

SPOILER ALERT

SPOILER ALERT

HOW TO GET THE WEDDING

So many people have complained that they have missed out on the romance/wedding storyline, that I thought I'd post what I did to get it. I'm not saying that this is the only way to get it, but it is what worked for me.

WARNING
If you are already married to someone, using the vanilla system, Astrid WILL NOT romance you. Also, if you have ever been married through the vanilla system, even if you are now divorced, Maramal will not have any dialogue for marrying Astrid, and you will have to resort to console commands.

Here then are my tips for getting the good ending. Obviously, if you don't want spoilers, and want to try yourself, don't read any further!

You can also kill your spouse without Astrid noticing it. This should give you option to romance her or tell Astrid about your spouse demise if she has already seen he/she before.

Dye For Astrid Quest
Offer to find the ingredients for Astrid. DON'T send her off on her own to find them. At the end of the quest, agree to take Astrid sightseeing.

This wasn't mentioned by Beanbagels, but to get romantic ending you have to hear the line about glacier. It is one of responses on "Tell me about yourself" (it becomes available later).

A Stroll Around Skyrim Quest
In the Eldergleam Sanctuary, Astrid will ask "What about you? Does this tree please your eyes as much as mine?"
Reply with "Standing together with you in the shadow of it pleases me more".
Astrid will get pissed off at this, and say that you have ruined it! This is where I went wrong before, as I thought I shouldn't have made her angry. So I went with the other line, something about "Mighty One", and ended up friend-zoned. So, trust me, go with the "Standing together" line. All will be well. True.

The Letter Quest
After the 3rd lesson, at the campfire, tell Astrid "I'll walk with you".
Next use the line "Duty seems to be really important to you. But I think I feel.... rather interested in you."
Then "I don't know. Like my heart skipped a beat when I saw you first time. I felt a little spark in my chest".
Astrid will get angry and, after her "cautionary tale" about when she broke someone's nose, choose the "Kiss her" option.
After she has punched you in the face (lol), apologise to her, then take her to Solitude. Punching is not needed, actually. This option doesn't affect your romance at all, you only need to express your feelings.

Drink & Brawl Quest
When you have the fist fight with Astrid, it makes no difference whether you win or lose but, DO NOT CHEAT (i.e. no weapons, and no magic, even though she uses them!). You can also skip the fight with no consequences.
If everything goes according to plan, Astrid should take you to lie down and look at the stars. She will have some romantic things to say to you, so don't cut her short. Encourage her with "No, no, continue" then, finally, "Thank you". This option doesn't change anything.

Everything from there should be plain sailing and, once you have recovered the fleece, Astrid should propose to you.