Oooo that's a toughy. Every woman is different so finding the right thing to say is an almost impossible feat. BUT, just starting up a conversation with her is half the battle.
(Disclaimer: I am just speaking from personal opinion and experience)
It's best not to start the conversation with a compliment on her physical attributes because that just screams "I WANT TO DO YOU" to most women. Instead start up on conversation based on the your environment. If you're in class then ask her about the homework or wow her with your best impression of the professor. If you meet her in a coffee shop ask her if she's tried the new "(insert outrageously expensive mocha drink)." In many cases, the conversation will lead to more substantial subjects, but your goal at first is to simply get the girl talking.
ASK THE GIRL ABOUT HERSELF! Good for 2 reasons: 1) Women like to talk and this feeds our ego 2) it gives you a chance to found out what you 2 have in common, it may even open the floor for a possible date. For example: The girl says she loves the Coen brothers so you invite her to dinner and a movie.
Make sure you're dressed to impress. As shallow as that sounds, it's true. I know within the first couple of seconds of meeting a guy whether or not I find him "doable." If you're not dressed well I will probably hesitate to put you in my "wonder what he looks like with his clothes OFF" category. Your clothing is an extension of your personality so let it shine! I don't mean you should be wearing the $70 Ed Hardy underwear under your 7 for Mankind jeans and carry your Louis Vutton man purse...but you shouldn't be dressed like hobo either.
Finally, of course it's always important to be yourself. Women have a 6th sense for bull sh*t and we can very readily tell when you're not being sincere. Be truthful in your compliments. Really mean it when you say you think she's intelligent, hilarious, or beautiful. Don't pretend to be someone you're not. Case in point: My boyfriend is a big nerd who plays Warhammer and WOW 50% of his day, loves math, and is ~135 soaking wet. BUT what I love about him is he never compromised who he really is to be seen as the cool guy. That right there speaks more than any glib, vacuous, and insincere pick-up line I've ever heard from a hot guy.
Good luck!
