As a male, get Morrigan to favour you enough to have a roll in the hay at your camp. This is probably also the first of the romances you will encounter. Although Morrigan has an outlook on life at odds with most npc's you run into, you can always try removing her from the party when you know she will not approve of the outcome.
Focused on early, this can be achieved after completing Lothering without any special plot gifts. Save up your gifts and lay it on her, starting with the Golden Rope Necklace, which will boost her liking of you by 8-10. Jewelry and alchohol works too (1-4). After that she will have warmed up to you enough to carry on through most of the conversation trees. Save your game first and talk about everything available. Morrigan can be a bit tricky to figure out, but reload if you get a negative outcome.
Once she likes you enough, you can talk to her about "something personal", and try kissing her for a last little boost. Once you finnish Lothering, look her up in your campsite and play coy.