Just like in the majority of BioWare games, love relationships are an important and complex element of Dragon Age: Inquisition. It is best to get prepared for romancing NPCs already at the beginning of the game, because this is a time-consuming process that requires you to take many correct decisions. Throughout the beginning of the campaign, there is not much going on when it comes to this matter and only later things get in full swing.
First of all, the character that you want to romance with needs to have a high level of approval for you (based on your decisions in dialogues). Unfortunately, there is no way to look it up so the entire process is intuitive. Additionally, each time you visit Haven and, later on, the Skyhold after completing a main quest, talk to the specific character. Ask about current events, as well as personal matters, e.g. where they are from. Agree, be a yes-sayer and keep an eye on the available options. Occasionally, one marked with a heart will appear, which suggests the character's disposition towards you (at the same time, such an answer is never negative to approval).
Once your approval level is high enough, the "special' category of dialogue options appears. To be able to go from words to actions, you will still have to do several favors for the character (a tactical map operation and small quests in specific locations). It is worth noting that not all of the characters agree on a relationship if you are already involved with someone else. Of course, you can always break up with the previous one, but this will affect their support for you.
The table below informs of the sexual preferences of the individual allies, who your character can romance with. On the following pages of this chapter, you will find information and hints concerning winning the favor of the individual allies. Following pages also provide information on minor affairs and the "moments" with individual NPCs.
Women of a given race
Cullen (humans and elves)
The Iron Bull