Well, there's not really any for sure way to approach a girl. I mean, "Hi, how are you?" is pretty much your best bet, but every girl is different. Yeah, almost all girls are gonna be able to tell if you're a nervous wreck, so like others have said, be confident in whatever you decide to go with. I would like to say something, though. Some girls may think it's kind of cute if a guy is nervous/shy when he talks to her for the first time; however, there's a difference between being nervous about talking to a girl, and not having confidence in yourself. You gotta be comfortable in your own skin because no matter what you do, you're stuck with it. Not even plastic surgery can change who you really are. Do whatever it takes to feel confident (not proud, confident) in yourself. You could buy a new outfit, get a different hairstyle, maybe even work out more if that's what you gotta do. Just be happy with yourself.
I think I should also point out that there's also a difference between a good self-esteem and impudence. Don't be to proud of yourself 'cause you'll come off as an arrogant snob. Those guys who think they can snatch a girl up with a one-sentence pick-up line make me sick. If you wanna be friends with her, and eventually maybe even date her, it's gonna take time. Show her you really care about her, and that you're not just talking to her just because you think she's hot.
Basically, be ready; don't get cocky; don't be creepy, and most importantly, remember that she's a person just like you. Good luck. ^^