Since you guys are in a classroom setting, this actually plays to your advantage. Does your professor ever break the class up into smaller groups? I've had profs who break the students into study/homework groups to get a head start on the workload. They usually let the students assign themselves, and most people group with those nearby. It's definitely helpful that you've made a habit of sitting near her.
I'm trying to think of what worked on me. I've hung out with several guys from class before. Honestly, they were sitting pretty close to me; maybe 1-2 seats away. And they had some pretense to talk to me. If we weren't in an in-class study group, they asked me for a pen or something. And when the class was dismissed, they looked over and casually said something like "So, where are you off to?" or "What's your next class?" I had lunch with a guy once because I didn't have anywhere else to be and he didn't either, and he seemed like a nice dude.
Then once you guys are talking, just get to know her. Who she is, what she's interested in/doing with her life. Hopefully you guys click. No matter what, don't force it. The reason most guys don't get the girls they want - and vice versa - is that few people are really attracted to each other. If there's not a natural, mutual connection, it can't be forced. In that case, off to the next person. =)
Another tip, specifically for getting someone's number in class. I've used this several times myself. Sigh and say, "Ugh, I forgot the homework last night. I wanted to call someone in class, but I don't know anyone. Do you wanna trade numbers?" Doesn't need to be verbatim.
srsanswer/10 YEAAAH.