I had a difficult time with this one on my first playthrough, and actually ended having to back track a bit, so I thought I'd leave a few tips here that helped me. There might be spoilers to follow, but I'll try to be vague.
Sera's approval has to be fairly high to get her romance, so if its not firing, you probably just have more approval farming to do.
There are bugs that can occur if you don't complete the romance before Wicked Eyes and Wicked Hearts (or at least there were, not sure past the most recent patch) which will prevent the romance option from appearing. So its best to pad your approval before then.
You don't have to get all of the major story approval decisions right, but you are going to want to get the majority of them. Some tips: conscript instead of ally, accept the inquisitor title in the name of all people, conscript instead of banish, keep everyone alive. For the record, I missed on the first of these, and still got there. If you've got RP reasons for doing things differently on a few of these, you can still get the romance, but its quite a bit more work.
Being too "elfy" really annoys her. Keep that in mind with dialogue choices.
Several Hinterland quests gain approval from Sera. I don't remember them all, but I do remember the wedding ring quest.
I'm pretty sure every flirt option nets positive approval.
Flirting with Scout Harding is probably the easiest way to boost approval with Sera. It seems counter-intuitive, but it works like a charm. Have Sera in your party every time you open an area and flirt with Scout Harding each time. The flirt option with Scout Harding only appears for areas that open post-Skyhold.
Being a hanging judge will usually get you positive approval with Sera.
Side with the common people over nobility every chance you get.
There are three character quests that must occur before the romance will fire. These are the prank quest, the Verchiel March, and the conversation on the roof. Again, you'll increase your odds if generally side with Sera and treat her well.
You must complete the romance before What Pride Hath Wrought. There are story reasons for this.
I hope this helps someone have a slightly easier time.