How do I talk to this really, really shy girl?

I have this girl in a few of my classes and she doesn't have friends in them and all lonely so I come up and talk to her. I really want to be her friend she seems like she would be really cool and she's pretty too. Also, she's friends with people I know and I've heard that she's outgoing and funny. But when I talk to her she doesn't really respond and just nods and smiles, and she gets really nervous like she fidgets and stuff. When I say hi to her each day she just gives me this cute smile and looks down. I want her to start talking to me and not be so shy because I know that she would be an awesome person. How should I go about this?