I agree with Racing Rice, the best thing is to just be yourself. Girls don't like when guys fire cheesy pickup lines at them. At least I don't. "Hi my name is...., what's yours?" works for me. Or start out with something funny that will make her laugh. I like guys with a sense of humor!
As for girls "throwin smiles your way"....I know from my point of view that I definitely give a guy a smile when I think he's cute or I wouldn't mind talking to him along with some serious eye contact.
Because I'm shy, that's my way of initiating something.
