Don't be needy. Be nice. Tease her playfully. Sit beside her. Smile but don't smile too much. Say something nice about her but nothing too nice, make it an unintentional compliment("What's that smell? Smells nice... Oh, it's your hair/perfume").
Just be nice when building comfort. Tease her a bit and be playful. Also, Kino!
http://www.youtube.com/watch?v=kmZa-dtruFI
If she's shy don't escalate too quickly or you'll scare her away. In fact don't escalate much unless you're in a social environment(A pub, club or party). Focus on building comfort and rapport with her by being playful, teasing and poking fun at her but in a good way(Don't neg her! You're just poking fun and not bringing her down at all, she needs to know whatever you say when you do this is totally not true!!). Focus kino on her arms, shoulders and hands. A sure-fire way to touch her hands and arms in class is to mess with her and say you want to do something. Grab her hand, take a pen and write penis on her arm or hand. When you do this laugh and gently pat/rub her shoulder. It's childish but it works!!