It s got to grow to the point where it seems comfortable, acceptable, for you to tell her your name, have her tell you her s, etc. If you ve gotten this far and she seems friendly and open, congratulations, if not, don t worry about, try again with someone else. At this point, if it feels appropriate, start asking questions about her, which school she goes to and other personal but not too personal information. You can only hurt her impression of you by doing this, most of the time it won t lead her to think you re modest. On the other hand don t be a braggart, be truthful and confident about the truth.
Confidence when dealing with anyone is always important, girls especially.
Now you ve reached the end, there s nothing left to do but pose a question which will probably lead her to the conclusion that you have romantic interest in her. Besides for the initial contact, this is probably the hardest part as you re almost but not quite asking her out. The thing to remember is that if you don t ask her, and you don t see her again, you ll have no chance. If you ask her, there is a chance. If she says no, or another form of dismissal, accept it.