First off, don't do it. Just don't. Seriously, what kind of idiot intentionally puts a flaming torch into their mouth?
However, since I am that kind of idiot, let me tell you some things you should know if you insist on being that stupid.
First, don't, under any circumstances, pick up a torch if you're drinking, or stoned, or in any other way not thinking straight. That kind of thing will land you in hospital. Don't do it alone, either: there has to be someone present who knows what you're doing and is ready to extinguish you if you set yourself on fire in an unintentional and uncontrolled manner.
Second, pay at least some attention to your immediate environment. If there's a strong wind, you probably shouldn't be playing with fire, if you can even keep anything lit. It's possible to eat fire indoors, but you'll need a big, well-ventilated space - there are better ways of getting to know your local firefighters than setting off the fire alarm.
Third, you really should find someone who knows what they're doing to teach you. Like any other skill that potentially involves significant personal risk, it really has to be taught in person by someone experienced.
For eating fire, as for fire spinning, the preferred fuel is white gas. It burns relatively cleanly and - on the scale of flames - quite cool. You can transfer fuel and flame off a lit torch onto your skin, and while you'll feel the heat, you have several seconds before it will cause a burn. At least in the US, it's readily available anywhere that sells camping supplies - it's the same fuel that most backpacking stoves use. Wear natural fabrics, leather, or leave your skin bare: wool, cotton, linen, and silk take several seconds to catch fire, and can be put out easily. Synthetic fabric will melt and stick to the skin underneath - I've caught a spark from a campfire on the synthetic upper of one of my shoes, which melted and left a burn out of all proportion to the spark.
You will at some point get burned doing this, but as long as you're reasonably careful probably not badly. If you don't get the angle quite right and catch your lip on the metal of the torch, that will leave a small burn. More common is a scalded tongue, much like the effect of taking a drink of too-hot coffee.
An eating torch is a small Kevlar wick wrapped around the end of a metal stick. Note that the metal will absorb heat as long as the torch is lit; the part closest to the flame will end up very hot. The basic principle of eating fire is to bring the wick into your mouth and close your lips around it until the air is choked off and it goes out. In practice, it goes like this:
Lean back, tilting your head back so you can hold the torch vertical as it enters your mouth
Take a deep breath in and hold it
Lower the lit torch into your mouth, guiding it in with your tongue if that helps, and close your lips around it just below the wick
Remove the torch and exhale
That's the correct way to extinguish the torch. Especially starting out, it's easier to get the torch into your mouth and blow it out, which works and still looks impressive to the audience.
If you seal your lips around the wick as you withdraw the torch, you can trap some of the flammable vapour in your mouth. Let this out slowly through pursed lips, and you can light it, producing a flame floating over your mouth. Light the now-extinguished torch from that, and continue. In all cases, make sure to exhale hard at the end of the trick, to clear out any vapour from your mouth so you're not breathing it in.
From a performance point of view - since most of the reason to do this in the first place is to show off - eating torches will usually burn for about two minutes, maybe a little longer, so a fire-eating act will be fairly short compared to some other fire props. If circumstances permit, it's fun and looks good to add in some skin transfers and other tricks - but in the end, you're putting out a flame in your mouth, and that's a pretty good show all by itself.