How to help her fall in love with me?

[Mark]

There is this one girl. She is very shy (I have never seen her talk to anyone before, I am shy as well), she talks to herself sometimes which is really cute. She is in 3 of my 4 classes, each class being 84 minutes long. I am in 10th grade.

She sits two tables ahead of me in Science. She sits in the centre of the room for computers, whilst I sit on the left side. She sits at the same table as myself for art class. She is directly across from me in art, we are close enough to touch.

I'm very shy and a bit awkward sometimes. She made a very amazing painting today and I was going to compliment her, but I have my friends on both sides of me, I was worried they would think I was being weird.

I haven't actually talked to her before (Fail on my part, I'm scared people will judge me or she'll end up hating me), though I almost did today at the end of computers, as the teacher usually tells us to log off and everything and people get up and converse for the last couple minutes.

I want to get to know her. I want to be her friend and eventually her boyfriend. We are both shy, however I've never seen her hang out or talk to anybody. I have 2 or 3 friends in total.

Is there any way I could get the courage to talk to her? How to win her over once I do?

Thanks;
Mark.
Note: She doesn't have a facebook, I've checked XD And as it's the weekend, I have no way of contact with her as of yet.