As funny as it seems I noticed that the most efficient way to approach any girl for me seems to just smile and say something like "Hey, what's up?" to her. Even if I can't come up with anything to say at that particular moment, if the girl is friendly she will usually help you out with getting the convo going. Also, for some reason, it seems that when you say that to a girl once (even when you don't go into a convo at all), she will greet you everytime she sees you afterwards (if she remembers you).
Two days ago actually, as I got into an elevator and was going to eat breakfast, a pretty girl walked in and started looking at the floor shyly. I smiled at her and said "Hey!" in enthusiastic way. I didn't need to say anythign else afterwards, she smiled at me and said "Hi, My name is ...". Seemed a bit weird to me that she just threw her name at me like that, but I decided to do the same so I told her my name. After that there was an awkward silence again as I didn't knwow hat to say (partially cuz I was only half-awake). She went to the dining hall as well, and as soon as I got into the dining hall, she turned around and said "come sit with me, and my friends". So I went to sit with her, her roommate, and someone else, and the convo started from there.
BTW, if when you smile and say "hi" to a girl she doesn't reply at all, it's safe to assume that she is either a *****, or has other problems, or she didn't hear you, because even girls who seem unfriendly smile and say hi when you do the same.
