What can I talk about with a girl in my class in school?

The best way to approach her is to simply smile, if she smiles back you can walk up to her, if she quickly turns her face or whatever then its not the time.
The easiest thing to talk to her about would be the things you two have in commen. Comment on the lesson you took at the end of the class, ask her whether she likes this subject, ask her what is her next class. (I'm not so good in giving examples, but I hope you can get the message.)
Bust of luck,
Silent Breeze