The point of being a wing-woman is making the other person look cool. In its best form, it is a selfless act of love. I would go so far as to call it a spiritual act. You are completely focused on the person you are with. You laugh enthusiastically at their jokes and tell cool stories in which they play the protagonist. You get them more alcohol before they run out. Basically, you act enamored of them, and then, following your example, everyone else will be. Your goal is to set an example.
To initiate a conversation, pretend you are having an argument over something with your friend and you need an objective opinion. Extra points if the argument is over something sexual, because that sets the tone.
In this role, you are not allowed to be weird. Why would anyone follow the social example of a weird person? You must be perfectly charming and neutral. If the person you are targeting ends up sticking around, they will figure out you are weird eventually anyway. Do not talk too much. If the person you are wing-womaning for makes a slightly off-joke or extends their story a little too far, find a way to redirect subtly while continuing to act like they are the most interesting person in the room. Remember, this is an art. You do this for the joy of the art, not for your own attention. Your ego is not important. What is important is that your friend gets laid.
When it comes down to closing time, go away for a couple of minutes, then come back. If your wing-womaning worked and your friend has a new make-out buddy, they will probably disappear. If either party is not feeling it you can diffuse the situation and take your friend home for ice cream. You probably want your wing-womaning skills to work, but remember, your friend is the most important party here, and she needs to feel comfortable at all times.
This formula works for more than women. Men can use it, too. Also, it can be used beyond the contexts of romantic situations, though you should probably adjust the amount of sexual tension in your conversation accordingly. If you have a particularly shy friend at a social gathering, wing-woman until they have a large group of shimmering new friends around them.
Why you should indulge in the act of generosity? To hone your socializing skills, to make your friends happy, because it is more fun to focus on others than you own self-consciousness and because the universe will eventually return the favor. Trust me on that one.