1- Get the tire to a good "clear" area. It doesn't have to be perfectly flat, it doesn't have to be all sand or dirt. Use common sense...
2- Clean the tire bead(s) and rim with a GLOVED hand
3- Remove the valve core. (You don't have to do this but it allows more oxygen for combustion. I've also seen a valve core or 2 shot out of the stem from over-zealous use of either.)
4- Get your starter fluid and "flame maker" handy. Stand on tire giving a short little "squirt" of either at around the 12, 3, 6, and 9-o'clock positions. (You're standing on the tire to open up a gap at those positions to get your fluid IN the rim/tire cavity.)
5- Make yourself a "wick" by squirting a strip of fluid from your last "squirt", to tire surface, to ground if you like. Step back and light her'up! (When it's hot out the starter fluid will evaporate quickly so you have to be ready with flame or you'll waste fluid and have to do it again. In colder climate you have a bit more time but then have to deal with slower ignition because you lose the fluid evaporation needed for combustion.)
6- Now. One of two things will happen at step 5. Combustion will happen and you'll hear a nice big "POP", the tire is seated and friends will think you're magic OR the tire and will just sit there burning some as the the evaporated fluid and flame isn't getting enough oxygen for good combustion. DON'T sit and watch it burn. Your tire wont burn up but you'll have wasted fluid, flame, and time which are precious commodities when your out in the middle of nowhere with only 3 useable tires on your truck! Do yourself and the tire a favor and quickly stomp on the top of the tire if it's just laying there burning. Stomping opens up a gap in the tire/rim cavity for a split second allowing a burst of oxygen to complete the combustion necessary to seat the tire bead. DON'T kick the tire - why would want to kick a burning tire towards someone or something? That, and it does nothing to allow that burst of oxygen in.
At our school we have taught this to every civilian and military class we've had. I've had everyone from 60 year old men to SEALs do it. In the 8 years I've taught it (been doing it longer than that) I have NEVER seen any one of my students even close to hurt. Like anything else - use your head. It's effective and it's fast and it's a skill that's damn good to know!
(I'm not exactly sure why you would ever need to get your air chuck immediately on the valve stem right after combustion or "Pop". You do need air to fill your tire but you have all day after the bead is set to do that if you want. I'm not sure what Metcalf is getting at here. You DO NOT need compressed air to help the combustion part of this exercise. You DO need air to fill your tire when done though.)