I'm quite taken with her. I don't talk to many girls to be honest. You could describe me as shy, quiet boy who minds his studies. Anyway, none of this really matters. I'm quite a coward actually. As Gandhi once said "A coward is incapable of exhibiting love; it is the prerogative of the brave." So yea. I've never approached her before; she's most likely unaware of my existence as a human being. Point is: how do I approach her? What do I say? I know I should say "hello," or something, but reality is I don't see her very often. I maybe pass her in the hall, or see her walking to her next class, but that's it. I don't have time to get to know her during the school day. Any help would be appreciated. I thank you in advance.
But whatever you do, don't sound like you rehearsed it beforehand, even if you did.
Agreed, just be natural. don't treat her like a pretty girl like your infatuated with. Just treat her as another person that you wanna become friends with, but don't. If you treat her like a person and not just another pretty girl that your crushing on she'll realize it. Then she may open up due to the casualness of your approach. I third JonE's statement though.