I'm not a very good flirt. Within a relationship, I think I can flirt fine. It felt like it came naturally. Outside of a relationship, I'm learning. Here's what I think I've learned so far. Correct and add to it.

1) Flirting is talking about each other. It's not talking about yourself. It's not talking about other other people. It's talking about her and she's talking about you.

This is why "what's your sign?" (and in Japan "what's your blood type?") have often been used as ways to start flirty conversation by both men and women.
It get's people talking about each other which keeps the focus on the two of you. It gets you defining each other which shows interest, boldness, and can push while you pull.

2) This is from Juggler. Flirting is the opposite of sarcasm. I think this is a great definition for geeks. We know sarcasm. Flirting is saying "I hate you" while you really mean "I want you."

In this way, your body language, kino, eye contact, and vocal tone can all indicate "I want you" while your words say otherwise.