Help? How to attract and talk to this girl i like?

There is this girl i like in my class, she kinda doesn't know me. When i am late to class she always says hi to me. I get nervous around her and i put my head down on the table. she sometimes say do you have any work to do or do you have a pencil if i don't have one. And i just don't answer her, i feel nervous. We often make eye contact at each other and often she ignore me. She is really pretty and a nice girl. I really want to know her and i just don't know what to do. It been like over a month that i like her and i all i done was nothing. I'm a really shy and quiet guy. I just don't know if i have a chance. She seems to like what she is doing and work hard. Once when i was going to the toilet i saw her with her friends walking and she said hi to me. Sometimes when i look at her see quickly look away. And last week in class when i am sitting doing my work she came and get a worksheet or something and when she try to get through i feel her arm on me behind my back. And yesterday when she came in class i look at her and she look at me then she get her work and sit down at her table then i continue doing my work and i saw her look back at me. And today in class i saw her outside playing with boys and girls out there and i saw her touching other boys there and i don't know. It makes me feel bad and sad and i guess it is over. I don't know if i should move on or not. Help?