If a girl makes excuse after excuse for not being able to see you, you should take it as a sign that she's not interested and wants you to leave her alone. The odds are that she's not going to flat-out tell you that she doesn't like you, as that would hurt your feelings. But if she has to wash her hair on Friday, babysit Saturday, edit her short film on Sunday, bake cookies on Monday and so on, then you should probably assume she wants you to leave her alone. If she's interested in you she'll reschedule her events for you.
If a girl is into you, she either won't see other guys or won't tell you about other guys she's seeing, because she won't want to jeopardize her chances with you. However, if she constantly talks about other guys or tells you about her dates, then she sees you as more of a friend and less of a potential boyfriend. In other words, leave her alone.
If you have to text her, call her and leave four voicemails over three days in order to get one email back, she probably wants you to leave her alone. Think about how you treat other people -- do you decline to get in touch with them for days when they call you? She probably doesn't either, in general, but if she wants you to leave her alone, she will take her time getting back to you.
If you take a step towards her and she takes a step away, she's putting a physical distance between you and her. The same goes for edging away on a couch, not taking your hand and generally avoiding intimacy. If she wanted you to be around her, she wouldn't mind you being close to her and touching her. If she doesn't want you around, then she will make a point of keeping distance between you.