If your Shepard is female…
Option 1: Jacob
The most obvious choice for a female Shepard is the human Cerberus operative Jacob. He’ll act coy at first and not want to step over the line with his commander, but keep showing interest and he’ll finally admit he’s into you. The only downside to courting Jacob is that if you sleep with him, Cerberus might wiretap your vagina (see Mordin’s wacky sex ed talk on page one).
Option 2: Garrus
Keep up the friendly dialog and personal questions between missions. Eventually, you'll have the option to ask him about how Turians prepare for high-stress assignments. Keep asking follow-up questions on the subject till you get the option to suggest that you blow off some steam together. He's caught off-guard, but then gets into the idea. You'll still have to convince him that the interspecies thing is cool with you, but be persistent and he'll drop by your quarters with a jug of wine just before the final mission.
Option 3: Thane
Explore his past as an assassin and chat about his family and religion. When he thanks you for being a good friend, tell him that “friends” is a good start. He'll be intrigued, and open up to flirty dialog in later scenes. You'll know your relationship is maxed out when he starts talking about what he wants to do after the final mission. When he turns up for the final love scene, be sure to tell him you’re worried about him or he’ll leave without smooching on you.
A note on Jack and the ladies
Jack will talk intimately with you and reveal that she has batted for both sides, but when you try to take it to the next level she says she doesn't want to be part of the "girls club." If you try to pursue it further, she'll accuse you of "just pissing around." Sorry, lesbian gamers: nothing to see here!
Next page: Subplots that swing both ways