There is definitely an art to flirting, and most of it doesn't involve words. Most of our communication is body language and tone. Especially for women, who are not socially enabled to begin the verbal part of a courtship, flirting without talking is especially important. I believe that it is the woman who makes the first move in any seduction; the man only speaks first. To flirt without talking is an essential skill to attract the man you want. So here's how to flirt without talking.
To flirt without talking, one must have mastery over one's body language. Your prey (future date or husband) will most likely start physically far away from you. So the first step to flirt without talking is to master the eyes. Have you ever noticed that you can immediately lock into someone's eyes, no matter how far away they are, and you always know when someone is staring at you? Use this to your advantage -- lock eyes, hold for a while, and drop them with a smile to show submission.
After you make eye contact, if he's a good man, he should still be looking after you drop your eyes. Look back up at him. Give him the once over again, then turn away with a flourish. Show off your grace and poise and play a little hard to get with your body. Your back should be to him now. To flirt without talking, you must make him want to know more. This will draw him in.
The back of your shoulder should be facing him at this point, and you should be able to keep an eye on him over your back. However, do not stare. He should begin making his way towards you through the crowd, and should be relaying the energy of lust so powerfully that the crowd splits in two like the Red Sea at his passing. If this happens, you've got a keeper. Wait until he gets close to you, then turn back around. End up with your body a bit closer than is normally comfortable for friendly conversation.
You still do not speak. Your body should be barely touching his, your finger at your lip, your lip slightly smiling, inviting. To flirt without talking, you must get him to talk. Move closer millimeter by millimeter until he gets the nerve. Or loses it. By now his mouth should be open and he should be stammering something about a drink. If he is worthy, accept. Then see what he has to say.