Very carefully. No, I'm not being a smart aleck; fire eaters, from fakirs to sideshow performers, have very few secrets about their craft. Urban legend has it that fire eaters use "cold flames" that aren't hot enough to burn the skin or coat their mouths with fireproofing chemicals, but any flame from any source is hot enough to burn the mouth (how many times have you burned the roof of your mouth on something as innocent as piece of pizza?) and applying flame-retarding chemicals to the mouth can pose health risks. The tricks of the trade are precision, practice and the knowledge of one simple law—heat travels upward.
[A quick disclaimer: I am not a fire eater, and this is not a fire-eating lesson. I am a writer, and this is an explanation of how professional fire eaters do what they do. You should not use this article to practice fire-eating at home, and if you do, you cannot blame me or mentalfloss.com when your spouse/significant other/roommate/landlord/legal guardian asks you how you burned the place down. Now then"¦]
Fire eaters don't literally eat fire. They place flames in their mouth and extinguish them. It's like snuffing out a candle with your hand, but more impressive. During their performance, the fire eater has to remember two things: one, fire and hot air move upward, and two, don't inhale.
A fire-eater starts by taking a wide stance to keep her* balance and tilting her head back while holding the torch above.
As she lowers the torch towards her mouth, the fire eater takes a deep breath and begins to exhale slow and steady. This slow exhalation keeps the heat away from the fire eater's face as she moves the torch closer to her face and places it in her mouth. With her tongue stuck out wide and flat, the fire eater places the wick of the torch (which should be cool to the touch—fire eaters often use Kevlar thread for their wicks) onto it and partially closes her lips around the torch in an "O" shape.
So far, so good. Now the fire eater has to extinguish the flame, and quick. There are two ways to do this. The fire eater can completely close her lips all the way around the torch, cutting off oxygen and killing the flame, or she can put the flame out with a quick exhaling breath. The second method is preferable for performances where the torch has been lit for a while and may be too hot to touch with the lips.
That's fire eating in a nutshell (though fire eaters have a number of other tricks in their repertoires, like vapor tricks, multiple torch eats and fancy extinguishes). It seems pretty basic, but to do it right and make it look good for a crowd, fire eaters learn the method and then spend years practicing. If this sounds like the kind of thing you want to make a career or a hobby out of, the Coney Island Sideshow School offers classes in the art of fire eating.
* I'm going with the feminine pronoun because 1. most of the fire eaters I've seen in my day have been women and 2. I don't feel like writing he/she every time.
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