Attractive girl at lunch. Help?

[Ryno Slav]

This one girl that sits at a table across from mine at lunch is extremely attractive. After finding out who she is, I followed her on Twitter and found that she's single and is interested in many things that I am. I can direct message her on Twitter, so how can I begin talking to her? All I need is her number and I garuntee I can win her over. I can't directly approach her at lunch because she's surrounded by her friends. I don't want to go up to her like a lost puppy, especially if she doesn't even know me. Any ideas?