IndomitableSam said:
Follow the script below, and alter to your needs:
"I've seen you around campus and I think you're very (pretty/interesting/outspoken/compliment it seems she'd appreciate). I don't want to be creepy, but is it ok if I give you my email address/number to text? My major is _____ and I (hobbies/sports/whatever so she knows you're not a loner or whatever you've seen her interested in), and maybe you'd like to come (watch/participate/etc) sometime? If you're interested, here's my email." And hand her a scribbled note. Don't ever have it pre-prepared. Creepy as shit if a guy pulls out something with his number on it. Just have some paper folded in your pocket, pull it out, rip off a corner and write down your number. Then it's up to her. Just be charming and casual about it, like you might ask other people, but you do really want her to be there.
Please, more guys, do this! Please? Pretty please? Or some variant. But just walking up, openly saying you think she's cool and suggesting a joint activity? Even if it's just coffee or something. It is SO nice when that happens.
Almost all the time if I'm interested in a guy I don't know, even if he seems to notice and like me (smiling, receptive body language etc) I always have to do the work! And even disregarding whether I notice a guy right off, there are still almost no socially capable guys brave enough to just talk to me. I'm pretty sure I'm not -that- unattractive. And you would be amazed at how attractive being confident and socially capable and PLEASANT can be. Because I do get guys hitting on me, and it usually consists of men who know how to flirt but are thirty years older that me or reasonably aged guys saying things like "Wanna hump?" or making vague creepy threats (I once had a guy accuse me of following him...because we were walking in the same direction down a main street, and say if I kept it up I'd "get what I was asking for.") Or asking me extremely personal questions, or invading my personal space. I also got hit on a lot during my brief stint at a college consisting of mostly male international students, many of whom were pleasant enough but couldn't accept that firstly dating one of the students, who I had enough power over for it to be a conflict of interests, was a bad idea and secondly I wasn't interested. No, seriously. I'm not interested. Asking again will not get you better luck, go away.
To be fair, some girls are just going to glare at you and say screw off, but not all of them. At the absolute worst I would tell a guy with this approach thanks but I am not really interested. And on the two occasions a guy came up to me and just asked me out I was super impressed.