OK- here's advice...
coming straight from a female perspective.
I think it's (as much as guys hate this word...) cute that you get nervousaround this girl! I'm sure she'd be flattered to know that you felt this way about her!
If I were you I'd ask my friend not to say anything just yet. Try to be friends with her 1st. TRUST ME HERE the best relationships begin as friends and then they have more potential to evolve into something more later.
Ask her her name (if you don't already know it)
Ask her what she's into,about her family,friends (chicks dig it when a dude is genuinely intrested in them.) Then ask her if she is dating anyone at the moment?? If so...{shucks} right? NOT AT ALL <---here's your big chance.

You get to be her sholder to cry-on when this dude is messin' up. Just let her do all the talking. Let her know that you're there for her!!
When she realizes that you are the sweet,caring, kind or guy that you really are...she's guaranteed to fall head over heels for ya'....trust me
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Everyone staring at you too huh? WELL...SMILE!