Torches are an important fire breathing tool.
Perhaps the best advice a would-be fire breather can get is, don't be a fire breather. It can cause serious injury or even death if done wrong. Even if done right it can cause health problems after years of performing this stunt. If you're really determined to be a fire breather it's important to use the right equipment. This will significantly lower your chances of harm.
Flammable Liquid
Flammable liquid is held in the mouth and spat out at the lit torch. There's much debate on what fuel is best to use, but two common liquids are kerosene and paraffin. There used to be flammable liquid sold particularly for breathing fire but this has since been taken off the market due to safety concerns. Until something like that comes back, should it ever, you'll have to make due with what's around.
Torch
A lit torch is needed to breathe fire. Fire breathing torches are available and are best. In a pinch you can also use a metal stick with a piece of cloth soaked in flammable liquid wrapped around it. Still, it's best to use a fire breathing torch. They stay lit longer and are more reliable. These torches can be purchased online. You're probably best buying them online as they aren't the kind of things you're likely to find in most stores.
Water
Keep water on hand to extinguish the torch once you're done breathing fire. Water is also helpful should something go awry. You might also want to have a fire extinguisher in case of major accidents. A first-aid kit isn't a bad idea either, and neither is a car and a map to the nearest emergency room. Fire breathing is by nature a dangerous activity and you want to be prepared for the worst. Keep these possibilities out of your mind while performing the stunt, but beforehand think the potential pitfalls through so you'll be in a better position to protect yourself should the worst occur.