There's a really cute girl in my class. How do I talk to her?

InvaderWeezle
Ok, so I'm a sophomore in college. I'm shy and I have Asperger's, so talking is pretty difficult for me. I've never had a girlfriend, and all of my crushes on girls have ended badly. Anyway, I sit right next to a really cute girl in my Fantasy Literature class. I'd like to try for this girl, but I seriously have no idea how to even begin talking to her. Approaching people is extremely hard for me, and even when I do manage to say something to someone I like, I'm completely unable to keep any sort of decent conversation going; I never know what to say. So yeah, any help I can get would be great!
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Update: Never mind. Turns out she has a boyfriend. Damn it, why can't there be a cute girl in college who isn't already taken?
There's a really cute girl in my class. How do I talk to her?
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