This is the same problem a friend of mine has. He runs out of things to say after "hi"
Then he just stares at them untill they walk away.
So, I was talking to him about what I did to p/u chicks when I was still single.
Here are my four tips to meet a girl:
#1 Smile
and make eye contact before you walk over.
#2 Open with a joke or a funny line. (I steal shit from movies most of the time)
#3 Be honest, tell her she is really good looking, you would like to get to know her, and maybe take her out for coffee or drinks or a good shagging.
#4 Once you have her digits, WALK AWAY!!! If you stay, you will only do something or say something to make yourself less attractive and you look desperate.
My wife says all of this is bull shit, but it worked on her. I walked up and said "What's happen'en Hot Stuff?" like Long Duck Dong in "Pretty in Pink" She laughed and said "Dong? Where is my Automobile?" And the rest is history.