1. Do it on level ground far from the house or any overhang.
2. Put the turkey in and fill it with water until the turkey is barely submerged, then take the the bird out and mark the water line. This is where you'll fill the oil to. This helps avoid having too much oil (wasteful, occasionally explosive) or too little oil (tragic, as the bird doesn't cook right).
3. Light the burner and heat the oil w/ the oil thermometer in. Your target temperature is 350, plan on this taking 30+ minutes, depending on your burner and the weather. It's amazing how much a light wind can increase this time.
4. When the temperature is within 10 degrees of your target, get the turkey (which you've patted dry inside and out, a nice dry rub here makes the skin yummy, your mileage may vary with injection, etc) ready. This is an UNSTUFFED turkey.
5. Have two people hang the turkey from a brookstick or something and carry it between them, this makes it easy to stay out of spitting range from the fryer when putting it in.
6. Immediately before putting the turkey in, turn OFF the burner. This removes an ignition source.
7. Slowly lower the turkey in. It'll spit and growl at you, taking a minute to put it in is perfectly reasonable.
8. Re-light the burner, figure about 3.5 minutes per lb. The oil temp will drop a lot because of the thermal mass of the turkey, so keep that flame on max. The hotter the oil, the less greasy the turkey.
9. Turn off the burner before extraction, use an oven mitt or something while hooking the turkey.
10. Once in the kitchen, LET IT SIT uncut for at least 15 minutes. This is called 'resting' and is the difference between a dry and stringy turkey or a juicy, delicious super bird.
11. Never bother baking a turkey again, because this will taste so dang great that you'll want to fry every time.
BONUS: If so inspired, this is a great time to make onion rings, blooming onions, deep fried mushrooms, etc if you're so inclined.