I have to agree to one thing. Girls simply hate being stared at repeatedly. Its creepy and uncomfortable at best. Sad that I learned this fact after scaring away some really nice girls in my University days :D
I think the best way to approach a girl is to first make a good impression of yourself over some time without giving any hint of showing interest. Then, one day, look at her in the eye and smile and thats about it. If she smiles back, you're in, if not then walk away, it ain't gonna happen.
Lol, best advice :)