*laughs* I find it ironic that I see 18 and 19 year olds as kids, when if I think back to that age when I was 18/19 and someone called me a kid, boy, they would have gotten a verbal beatdown.
Anyhow, to your question, I would say that you first need to break the ice. Common ways to do this are by saying, "Hi" when you sit next to her, and asking to borrow an eraser or some such during class.

You know, stupid little things just in order to get you guys talking. Assuming things don't go horribly wrong, like you accidentally stab her in the eye when returning the pencil you borrowed, pursue things if she seems like a nice person.

After class you can ask her if she wants to grab a drink somewhere, maybe a campus coffee bar or something would do and just talk general study things.
I don't want to read anything in to the sitting next to you. Maybe like the first girl who moved away, she is also moving away from someone.

So don't stress about that. In all seriousness though,
go with casual conversation first, and if you
feel that's receieved well, you can continue. If you get to the end of class before you have made any headway, you may be faced with making a big step, like just asking her out for drink.
All the best,
Digit