I was terrible at this when younger. When I was about 16 I had a girl doing all kind of odd things, like coming over to hang out etc and I was just confused by it all. I was saved by the best friend network. Her best friend told my best friend she liked me but I seemed either disinterested or oblivious. My friend then came and punched me in the arm and told me in clear terms what was actually going on at which point it hit me like a ton of bricks and we did end up going out. Was astonishing to me though how obvious she was being and I somehow did not see what was happening. It made me wonder how many other cue's I missed as I did not date a lot. It can also be dangerous though as some women are just naturally friendly and you can misinterpret friendly for flirting and make's it uncomfortable.
Probably the best lesson I learnt about how to ask a girl out if you are really not sure is can you check with a mutual friend who knows both of you and likes both of you? Outsiders are often more neutral, and can actually just tell you if the other person is in to you. Secondly if there is a chance she is not interested you do not want to appear to be desperate for her to say yes. That scares them off even trying if they unsure as then its uncomfortable to them to break it off with someone who is besotted when they are not feeling it strongly. One of the best lines I saw a guy use in that situation was literally something to the effect of "You are an incredibly interesting and fun person and I'd like to get to know you better. Can I take you out to dinner sometime?" It was said in a way that was complimentary, but also not overly intense. It also sounded spur of the moment with no clear dates or anything so that it does not sound like you pre planned or agonized over it for a while. If the answer is a no or fobbing you off it is then very important to not appear perturbed by it and to remain friendly as that again eases the fear that you are besotted in an unwelcome way regardless of how you feel.