I have seen a few tutorials on the net about fire breathing (fire blowing?) but none really satisfies me so I'm going to try to share my experience in this area. I'll start with the usual disclaimers, do not do this alone, do not do this if you are not confident in your reflexes, you can have all sorts of bad things happening to you ranging from irritation, to burns and irremediable lung destruction. However if done properly this can be quite fun and low risk.
I have been doing this for over 10 years now, but not professionally nor on a regular basis (unless you call few times a year regular), so all I say apply only to this kind of use. I strongly disencourage anybody to do that on a regular basis and for long periods of time in a row. In those 10 years I have introduced over a dozen of persons to it, and none of us ever had a single accident not even a single light burn (crossing fingers).
First thing to do is to buy an appropriate flamable product, this is probably the most important part as a wrongly chosen product can be extremly dangerous.
Flammable Liquid are usually sorted by their flashpoint temperature (at which they ignite in contact with a flame) :
a. Class 1 flammable liquid shall include those having flash point below 100° F (38° C). Some examples are: gasoline, naphtha gas, jet fuel JP-4, alcohol, etc. (100° F - 38° C); and
b. Class 2 flammable liquid shall include those liquids having a flash point above 100° F (38° C). Some examples are: varsol, some cleaning solvents, diesel fuel oil No. 2-D or 4-D.
You want to use a class 2 product and not a class 1, even attempting anything with a class 1 product is somewhere between irresponsible and suicidal. The main reason is that those products will not burn at body temperature unless they are vaporised. I have successfully used Kerdane (metal degreasing product found in supermarkets in France), Kerosene (parafine derivate, it is not jet-fuel, found in some US groceries), Petrole desaromatise (Car oriented shop in Quebec, Canada), lamp oil (various sports shop in the US), neft (found at the gas station in Israel, this is NOT naphta). These products traditional uses are cleaning metal pieces, lighting camping/garden lamps, you need to know that unless you want to explain in every shop that you are searching for a product to breath fire. You will pay for those under 2US$/l.
I have never used specifically designed products, nor white spirit nor diesel even if some people claim they are usable. Specifically designed "fire water" is usually expensive and makes small flames, diesel supposedly makes enormous flames and tastes extremely bad as white spirit does. Try to use products as pure as possible and stay away from lamp oils with additives.
Once you bought a few litters of a flamable liquid ( 1-2 litters per person is fine unless you are planning a long session), you need to test it before playing with it. Put some in a cup and try to light it up with matches, if it does light up, you need to pick up another product. Taste it, after going through 2 litters I sometimes get a light nausea feeling but nothing bad, so if it tastes really bad you probably should find something else. It should be a little oily. Last test is to pour some on your arm (or any other part of the body you don't mind to burn :) and try to light it up, it shouldn't light up and should reinsure you quite a bit (obviously be prepared to the worse). Check if the product irritated your arm, i have seen a few people having light alergies, do not proceed farther if it itches. If it did pass all the tests you are ready to go and can call your friends for a night party.
You'll need to bring some form of torch, which can be made with any 50+cm stick and a piece of coton cloth (t-shirt) wrapped around (on which you poured some of your flamable liquid). Bring a big blanket (to stop an unwanted fire), a few bottles of water for practice, rincing your mouth, body and wetting the spots you fear to burn.
I suggest doing this before the start of the party, and not letting the persons already under the influence of alcool or drugs to get anywhere close to the fire. Head outside. Remove your t-shirt, pour some water on your face, attach your hair (beard and long hair has never been a problem for me), grab a bottle of water and practice a few times. Take your mouth full of water, a deep breath and vaporize the water (making a heart with your mouth like if you were going to do a big kiss). Water drops should go as far as 3 or 4 meters depending on the wind, always do it with the wind blowing from your back. After spraying all your friends with water, when you feel reasonably confident grab the torch, have someone hand you the bottle of flamable product and fill up your mouth. Give the bottle back, make sure there is noone within 10 meters in front of you, put the torch in front of your mouth (arm extended), take a deep breath and vaporize. You can remove the torch quite fast to avoid any burn risks on your arm (or alternatively have someone hold the torch like on Haggai's pic), the flame will light up progressively the vapors towards your mouth. Thebackfire speed depends upon the wind, how strong you breathed and the product but it is usually 1 to 5 seconds. Close your mouth and stop breathing when you want to stop the flame. You will get 2 to 6m flames depending on the wind, your breath and the product.
Do not swallow the product, nor breath vapors, even if not inflamated this is supposedly the biggest source of injuries. Clean your mouth and the spills with water and a cloth regularly, and have a big shower afterwise.
I suggest you to have a camera handy, this makes beautyfull pictures (remember to disable the flash). You can do combinations with several persons and one torch, but at 3 the temperature of the air start to be so high that it becomes really unsafe (but it is extremely spectacular to have a 5m fireball).
Other ressources on the net in french
here or in english
here and
here that I suggest you also read. Obviously, I do not recommand doing this based solely on informations gathered on the web, but some did before and are still in good shape.