The dynamic between people changes drastically if one person is romantically interested in the other. It can become hard to be yourself or to view the interaction objectively. You begin to analyse every word that comes out of his mouth, searching for meaning. Every gesture, mannerism and change in tone is critiqued to try to find out if the man in interested in you. Chances are, he will let you know by asking you out. But this isn't always the case. He may just not be confident enough to step up.
If the man isn't paying much attention to you, there is a reason. Try making small talk with him to see if he is just shy. If he responds confidently but doesn't try to further the conversation, you should treat that as a sign to leave him alone. If, however, he seems shy and doesn't try to further the conversation, then he might be really into you, but he is afraid of saying something stupid, or of stumbling over his words. Use your judgment to try to find out whether he is shy or confident when responding to you.
Generally, women expect the man to ask them out on a date. If you are sending him all the signals and he isn't responding by asking you out, you may want to give it a shot yourself. Ask him if he'd like to get together to hang out. If he says "No," that's a sign to leave him alone. If he says he's busy, but doesn't offer another time to go out, then he probably doesn't want to see you. If, however, he says "No," but suggests another time, you should treat that as an indication that he wants to see you.
Healthy relationships require chemistry. If there is no chemistry on the date, or you think there is but you aren't certain, wait until the end of the night. If he kisses you, then it's obvious. If he doesn't, he might not be that into you. Women generally let the man take the initiative, but if you think your man is shy, you could try making a move. If he doesn't respond, then you should leave him alone. The date is really a matter of testing the waters. If there is no response to your attempts to get closer, then he probably isn't interested.
If a second date wasn't set up while you were on the first, then there is a good chance both of you are wondering what will happen next. If he doesn't call for a few days, he is either giving you space for fear of scaring you off, he is only interested in occasionally dating, or he's not into you. Call him if you haven't heard from him in a week. If he doesn't answer or doesn't return your call, he probably wants you to leave him alone. If he does answer and doesn't want to set up another date, that is a key sign to leave the man alone.