She's pretty but what.

There's this girl named Lilly. She is in my study hall and sits 3 seats in front of me. When im working she looks at me. I asked her did she like me and she said no but later she said she liked me a little. Well an old friend came over to my table and started talking to me. I hugged her but when the girl left. Lilly started acting upset at me. So she left. She hasent told me she liked me. But always stares at me. I hear she is a shy girl. Sometimes I try to approach her but she moves and puts her head down. Ive complimented her and she seems so happy. I don't know how to approach her shes complicated. She flips her hair when looking at me and we only talk on Facebook. How do I approach her with out her freaking out and does she like me?

Start with a smile. If you see her looking at you, smile at her. When she starts to smile back, then say "hi"

Just ask her out. She is making it obvious she likes you. Ask her on FB so its not awkward and make it clear its a date so there is no confusion

Facebook is the weak way to ask someone out. If you want her to take you serious, ask her in person.
Asking someone on an initial date over the web is not bad IF it's someone you do not yet know in person.
You see this girl in the flesh.

Is she is too shy to go out, not much you can do. She probably does like you but if she cannot even TRY to work past her own social awkwardness, what kind of G/F is she gonna be?