Who may enter a love relationship with Solas? You can enter a relationship with Solas only if you play as an elf-female.
How to build positive relations with Solas? During all of the conversations participated by Solas (regardless of whether you talk eye-to eye, or with more characters ), pick the dialogue options that showcase your refined intelligence, your support for mages and broadly-understood interests in the surrounding world (particularly when it comes to the Fade). Also, remember to pick all of the dialogue options marked with the heart symbol.
Note - Watch your tongue while discussing elven customs, because you can lose favor points as a result of inappropriate commentaries.
More important steps:
- Building a relationship with Solas means having very long conversations with him, during which you should exhaust all of the available topics (especially ones that concern magic and the Fade). Additionally, during the main quest connected with templar/mage support, I recommend that you accept them as the Inquisition's allies, finally. Your relations with Solas gain momentum after you move to Skyhold - if you have developed your relationships with him to a sufficient level, you are up for a gentle kiss, after you visit Haven in the Fade.
- You should start completing his quests as early into the game as possible. These are Measuring the Veil and All New, Faded for Her. It is worth noting here that the latter of the quests needs to be completed in the way that does not offend Solas, i.e. free the spirit turned into the Pride demon without killing it (destroy all of the summoning stones). Let Solas act freely, in the case of the mages responsible for summoning the spirit.
- While completing the Wicked Eyes and Wicked Hearts main quest, you can play a short prelude to the romance with Solas. The unique cutscene of the meeting with him starts towards the end of the game, after you have taken care of your business at the Mythal Temple.