The best way to flirt is to start with casual, friendly yet interested conversation. Some girls might enjoy corny pick-up lines or cheesy endearments, but the safest bet is to start out by approaching her as someone you would like to know better. Be sure to ask her about herself and discover some common interests.
Eye contact is a very important non-verbal cue that signifies your genuine interest. Pay attention to her cues, such as smiling, returning eye contact and adjusting her posture to face you. Instead of focusing on your own nerves, listen attentively to the girl and respond in a relevant way. For instance, if she offers a personal detail, share one of your own. If the conversation seems to have gone well, close the conversation by asking for her phone number or asking if you can see her again at a casual event such as a movie or lunch date.
For a really, really indepth guide on flirting see the Social Issues Research Centre Guide to Flirting.