Yeah, I'll just say this: Go up and be yourself, but don't try to be yourself, because you'll just end up amplifying your self-described "awkwardness" to a degree that isn't charming or anything. I mean, some girls like cute, awkward, Michael Cera-esque guys. Others don't. Just go up and strike up a conversation about something ordinary and non-offensive, and take off from there. Let her talk more than you let yourself talk; don't interrupt. If she likes something you like, point it out, but don't go off on how you're this movie's #1 fan or you watch every episode of this show on DVD.
My general rule for how to appeal to girls is this: Dress nice enough that you look like you care about yourself, shave (but not too often), don't overdo your hair (this applies to things like gel, combing, etc.; basically, don't look like either a choir boy or a jelly-haired ******bag), wear deodorant, and don't wear the same thing two days in a row. Axe or Old Spice is kind of necessary, I'm afraid.