I'd approach her and say something like (well, assuming you're in high school or something to that extent
)
"Hi, my name is _____. I know you don't know me, and I don't really know you, but I think you're really attractive and seem like a nice girl. I was wondering, would you like to maybe see a movie with me sometime? (look at her friends, smile) If ya'll (hah! i'm a southern gal so I say ya'll) would like to come, you're more than welcome to join."
NOW. here's the thing.
MOST decent girls, who are not stuck up female dogs, will probably admire your guts and think it's cute you were nervous to approach them and most likely will agree (maybe not right away, or maybe she will...just depends on the girl) By inviting her friends, you're making this casual (so it's not some pressure-filled date) and you're also showing you're genuinely interested in her, because you're acknowledging her friends.
IF she acts like a total...well, you know. then guess what, bud? she wasn't worth your time. it may be really mortifying, but I'll be honest, I graduated class of 2009 and I really could careless about any of the stuff I endured in high school. it's in the past, and life went on, you know?
best of luck, m'dear. :]
EDIT: unsure if you should add her on FB, depends on how private her profile is. If she's got a lot of it set to friends-only, I wouldn't because this shows she doesn't like to reveal much about herself/life to the world. If it's completely open for anyone to look at, I'd say why not. If she asks who you are/why you added her, say "oh, I think I had a class with you. we both go to (such and such school) thought it would be nice to keep in touch :] " you can sort of play it off like that.