Skip the pickup lines. Most of them have been made fun of for a reason. Begin by talking to her. The best thing you can do is strike up a conversation about something that you have in common, be it the drink she's drinking, a book she's reading or her pet dog.
Look her in the eyes. Pay attention to what she says. Yes, you've heard it many times, but listen to the things she has to say. The more you actually pay attention to her, the more you can find something in common to talk about.
Be polite. Common courtesy seems to have gone out of style, but most women will respond very positively to it. Hold the door, pull out her chair and offer to buy dinner. It will win you big points.
try to touch her, albeit In very non-sexual ways. Touch her arm at a party and put your hand in the small of her back as you walk her through a crowded room.
Smile. Make jokes and relax. The more relaxed and fun you are, the more relaxed she will be.