Flirting is one of those things that, done well, leaves both sides feeling absolutely marvelous afterward, even if nothing comes of it. It's a combination of flattery, touch, witty repartee, eye contact and body language that transmits to a person not so much that you find them sexually attractive, but that you find them incredibly interesting. You like being around them; you find them alluring.
There are some methods of trying to get a mate that call themselves flirting, but are not. Flirting never involves cutting a person down to make them feel less-than so that they will then crave your good opinion - that's just bullying. Similarly, flirting requires a certain finesse; if you come right out and just say "Wanna bang?" that's not really flirting, that's more just... well, we're not sure what the word is for that, because it isn't seduction either. Flirting also isn't about just showing off your money or your jokes or your big muscles.
The most important part of flirting is that it brings pleasure to the target. Whether you get their number or not - whether that was even your goal or not - they should come away feeling like their most desirable, enchanting, witty, interesting self. Fortunately, there are a lot of ways to achieve this outcome, and some of them bear an uncanny resemblance to the techniques of our friends in the animal kingdom. Which are yours?