If it's a packed lecture, I just sit right next to her (obviously you can't if there are already people next to her). If it's not packed, then one or two seats away.
If it's packed, I just say "wow, pretty packed huh?" just as an ice-breaker. Yesterday I had this enthusiastic little Italian girl reply with oh yeah it sure is packed, and there were even more people for the last one blah blah. Obviously if you get any kind of enthusiastic response to such a mundane observation it's a good sign. But even just "yeah, I know" is good enough -- afterall, it's only an icebreaker.
After, you can just sneak in some casual comments/questions. Obviously you're not really gonna get too deep into anything (especially not if you intend to actually learn anything), but just stuff to show you're an interesting/fun/exciting kinda guy (not boring!). One that I usually get a bit of a laugh with is if someone enters the lecture theatre really late, like say 20 minutes after it's started, I say sarcastically "just made it..." Again, it's just light-natured fluff.
If you feel that you are vibing with her, at the end of the class, just say, so what have you got on next, and if she says nothing you can suggest doing something, like just hanging out wherever people at your school hang out. Or if she's got another class, you can just tell her to make sure she says hi if you she sees you at the cafetaria (or wherever peope hang out), or, if you want, like if you really clicked with her, ask her number or suggest hanging out at a preset time or something. Or if you don't feel that you made much of an impression, you can still ask her to hang out anyway, just to practise getting rejected if nothing else. (Last one is still hard for me, so I know how it feels.)
