Vash the Stampede said:
Generally "asking girls out" is kind of over-rated. I'm sure BonsaiK is going to pop his head in soon and put it a lot better then I'm about to, but the whole "ask her out thing" is generally unsuccessful. If you make it a big thing, it will weird her out, especially if you don't know her to well, and then you'll just be that creepy guy who tried to get in her pants.
If on the other hand you do know her quite well, you also run the risk of her seeing you as "just a friend," in other words, the infamous friends zone. Here's my personal advice on how to tell: if she talks about troubles of any sort(e.g. boys, finances) , there is a good chance she is "just a friend." However if she giggles a lot, touches your arm or chest while speaking, or makes visible attempts to reignite conversations multiple times, then there is a good chance shes attracted to you and you can go for it.
However either way don't go up and say "do you want to go out?" Even if she is attracted to you there is a possibility she will say no out of surprise. Ease into it. Hey whats up? I was just listening to some , do you like them? I heard they're having a concert . hey you know what we should go to that concert.
One last piece of advice for that last thing: if you mention the thing you want to go do (e.g. coffee, concert, etc.) at the same time as asking her "out," she might still say know out of surprise. But if you go on a tangent and talk about something else in-between mentioning it and asking her to go, then she won't say no out of surprise, at least.
I hope that helps.