Flirting, it's fun, sometimes it's productive, sometimes not. But there are ways to enhance your chance of success from both sides of the flirting game, that mostly involve being polite.
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Lots of people like to flirt. I do. I'm a huge flirt. But there are right and wrong ways both to begin the flirting process and to end it. And most of the right ways involve merely being polite.
First, when you're gearing up to flirt with someone, your body language is just as important as what you're going to say. Try to be relaxed and casual. Tension either reads as desperation or creepy, and you'll lose before you're even out of the gate. If you have to, go into the men's (or women's) room, roll out your shoulders and shake out your arms. Smile, don't leer. Do not invade someone's personal space until they invite you to do so. The one exception to this rule is trying to be heard over really loud music, and even then, lean over, keeping your body away from your intended's until they indicate they'd like you to be closer. Invading someone's personal space when they don't want you to is a big no-no.
Second, what you say is incredibly important. Forget all those cheesy lines that Maxim, FXM, Stuff and Playboy feed you: they're crap and rarely, if ever, work. Try just saying "Hi, my name is ______. How are you doing tonight?" See how he/she responds. If they answer you cordially, then move on to, "You seem like a really interesting/neat/awesome person/guy/woman, and I'd like to hang out sometime." Seriously, that's it.
If you feel you must use some sort of "clever" line, there are a couple things to keep in mind. The first is, does it include any words you would not say to your mother or grandmother? Yes, I'm serious. I really don't condone rudeness to anyone, but if someone's pick up line details either a part of my anatomy or what they would like to do to me in a sexual situation, particularly if I've never met them before, all bets are off. It's rude, classless, tacky and just plain sexist. Don't do it. The next thing to consider is the frequency with which you deliver the line. If you go down a line of girls/guys using the same line over and over, particularly when they can all hear or see you, that's a recipe for disaster. And third, keep it short and simple. Particularly in dance clubs where it's hard to hear, nothing kills a line like having to shout it repeatedly into someone's ear because they can't hear it.
Ok, you've made your opening salvo. What now? Wait for a response. If your intended seems to respond favorably to your attentions, ask them outright if they would like to go out, don't assume they will just know that you are interested in them that way. You would be amazed how incredibly dense the entirety of the species can be when it comes to people finding them attractive. If the object of your attentions politely declines the chance to further engage with you, is clearly ignoring you, or even if they are outright rude to you, walk away gracefully. If they were polite back to you, there is no call for rudeness. And if they were rude, being rude back is not going to score you any points with anyone, and the object of your attentions has just demonstrated how unworthy of those attentions they are. Besides, if you're anything like me, you won't come up with the perfect response for about another hour or so. Just let it go.
This brings me to how to respond to both welcome and unwelcome advances. Again, the key is to be polite. If you are interested, then, by all means, engage in conversation with them, buy them a drink, let them buy you a drink. If you aren't interested in the person flirting with you, and they have been polite and respectful, return the favor. Thank them for their interest and tell them that you just aren't interested. No clever sniping, no "Are you kidding?" none of that. I find, "Thank you, but I'm already here with friends/someone," works pretty well. Or even, "Thank you, but I'm just not interested."
Here is where I'm going to part ways with a lot of people, but this is how I feel on the topic, regardless of which gender is in which flirting role. Take the approach as a compliment. This person obviously found you attractive enough to risk public humiliation to come talk to you. As long as they are polite and respectful, it costs you nothing to return that favor. Being rude to someone who has approached you politely and respectfully just makes you look like an ass.
A friend of mine told me this story about hanging out at a local coffee shop, and spending close to an hour chatting with a young lady. He had an appointment, so he thanked her for the conversation and left. After his appointment, he returned and she was still there. So he walked up and said, "You know, I really enjoyed our conversation earlier. Could I take you out for dinner some time?" Her response was, "You've got to be kidding." Utterly tacky.
Now, I am going to give you an example for the exception to the no rudeness rule.
Once someone has turned you down, go on your way. Do not keep pestering them with your advances. Persistence is not endearing, it is not cute, it is not desireable. And I don't care what teen movies say. It is stalker-ish, creepy and wrong. Don't do it. I'm serious.
On the other hand, though, as the flirt-ee, it behooves you to project a clear and firm negative response if you are not interested. I know, no one wants to be the bad guy, but sometimes you have to. If you truly are not interested in someone, do not let them buy you drinks and gifts. Tell them outright that you are not interested now and will not be in the future. For me, the level of rudeness escalates with each time I have to repeat myself. What starts out as "I'm very flattered but I'm just not interested," will work it's way to "I am not interested in you, please go away," and ultimately, "What part of fuck off do you not get?"
But really, there should not be any reason to reach that level of hostility, if everyone is polite and respectful. This means respecting the response of the object of your desires, and behaving accordingly. This also means respecting the person who hit on you enough to respond honestly and not try to take advantage of them for free drinks.