She is new and I'm falling for her.. What do I do?

This girl has been in my homeroom since last week and is amazing. She is beautiful and seems so nice but I have yet the courage or knowledge to talk to her. I'm always doubting myself over what to say. Today I was hanging out before I got on the bus for the ride home and she came over to talk to my friend and I have nothing to say to her... I really would like to talk to her to just get to know her better. What should I say and do when this happens? Anyway this Thursday I am walking home and I know she does as well with a few friends that I know and I'd like to say something then or even sooner if the hang out thing happens again. Please help.