Option one. You saw her. She noticed. You stopped looking at her. She looked back. You are a boy, she is a girl. You want it any more obvious? We both know that you need to ask her out if you want something to happen, though. There is a whirlwind of ideas in your head. But you don't know what to do. But now she is looking again, and that means you have less than ten seconds to choose if you want to go get that single or if you want to be considered a coward.
Option two. She works, studies or lives near you, or she has been your friend for quite a while (that is, you already know her name and you have already got her phone number, e-mail address and IM account). But something has changed. She has "grown up". She has gotten pretty. And she is still single. And you want to find out the rest, but... does she?
This sounds familiar to you, right? This happens to almost every man on this polluted Earth. That's not excuse, we know. We know you want to do something about it... and fast.
If you are like me, you should be already fed up of losing your time time reading pseudo-expert rubbish on how to ask a girl out or how to approach her in a disco or nightclub. The girl is single, she is there... now what? You should have already found out that usual pick-up lines do not work and that most of the flirty compliments you say are received by her mind either as a joke or just as a sexual desire that brings a defensive "get lost!" as reply.
Our advice? Pull yourself together. You are the man, she is the woman, remember? Think chauvinist, in the sense that you move, not her. Recover your manliness and get ready to use it to draw her attention and make her feel attracted. Are you feeling it already? Good. Just be careful not to exaggerate because arrogance is one of the major turn-offs a single woman can find. A little (just a little) of self-deprecation, as it is funnier, also works fine.
Be polite. If you behave manfully before the world but politely with a single woman, she will find you more attractive than men who do not. This attitude can help you a lot when approaching. A little chivalrousness can also be a plus... but it depends on what she is like.
Make her laugh, but do not say anything stupid. They are not synonyms (write it 100 times in a whiteboard, if needed). Also forget the idea of being cheesy or flatterer. Just be yourself. Smile. Say hello. Then continue.
Have a dialogue, not an interrogatory. Remember that you are approaching and that she is being approached. If you start making question after question she will feel invaded instead of invited. Keep the initiative in talking until you feel she has understood that you are here because you like her and not because you are a pervert or a psychopath. Once you feel her confident, start asking a little more.