How do you make friends and possibly a girlfriend out of a girl that barely knows you and that you really never get a chance to talk to?

ok so i am a girl and i can totally help. what cha do is you accidently like drop your pencil by her and be like sorry i got to grab my pencil. then she will probaly say something like ok or ill get it and when she does that you try to make small talk say something like oh i can be so clumsy sometimes or something like tht and then you introduce yourself but don't shake her hand you would seem wierd then after tht you could talk to her in the halls wave at her and stuff like tht when you think she isn't tense or wierd around that's when you start being more intimate by saying stuff like oh you look really pretty today yea just somethin like tht