I suggest you follow the instructions of the torch manufacturer. FWIW I crack the fuel and light, increase fuel to get appropriate feather, then add oxygen for neutral flame, then adjust flame from there. Note that when the flame begins to leave the tip, you have reached the maximum amount of fuel the tip was designed for. To shut down, I turn off the oxygen first, then the fuel. Some manufacturer instructions say to turn off the fuel first, some say to turn off the oxygen first, some say to turn off the fuel first unless the torch pops, then turn off the oxygen first. The pros and cons are as follows: turning off the fuel first will keep soot away from your tip. Turning off the oxygen first will keep the flame from burning back inside the tip and popping. The problem is that when you turn off the fuel first, you are leaning out the mixture. As the mixture leans out, the flame front burns back faster. If it burns back fast enough, it gets into the tip and pops.

Hank Process 1 is how I was taught, otherwise you risk a flashback into the handle. The newer torch handles this wouldn't be a worry but the older ones could blow apart.

Peace,

http://aws.org/cgi-bin/mwf/topic_show.pl?id=3478#13353
This is another thread which generated a rather amazing amount of discussion on this subject.
Edit- messed that up somehow- this link is correct.
Bill

I saw a Victor torch video that explained the procedure quite effectively.
Lighting the torch.
1) Open the fuel valve slightly and light.
2) Increase the fuel quantity until all the black smoke disappears from the fuel-only flame.
a) If the flame stands off from the end of the tip it will be harder to keep the torch lit when adding the O2. The danger in the amount of gas (fuel/O2) passing through the torch is when there is too little flow. The tip is cooled by the fuel gasses that pass through it. Too little gas flow will allow the tip to overheat creating the dangerous condition of igniting the fuen/O2 mixture inside the tip. This is noticeable when a) you hear the high-pitch shrill sound coming from the torch or b) the tip melts off. Both conditions are bad news. If you hear the shrill noise, Victor recommends shutting off the O2 valve and then the fuel valve. Allowing the tip to cool before relighting the torch would be a good idea (sarcasm added for dramatic effect).
3) With the smoke from the fuel only flame is gone, add O2 until the desired flame is reached.

Extinguishing the torch.
1) Close the O2 valve first.
a) This prevents the torch from popping. Popping, as explained by other contributors to your question, leans out the fuel/O2 mixture causing the pop and, according to Victor, deposits a small amount of carbon inside the tip creating a hazardous burn back potential. Another benefit to shutting the O2 off first is it tests the torch’s O2 valve. I have done experiments and have found I can’t see any difference in the flame when it is fuel only or fuel with a very small amount of O2. To check the O2 valve—read on.
2) With the O2 valve closed, close the fuel valve.
a) Now, in my opinion, is when you can check to see if both valves are closing completely.
i) Condition 1: Fuel valves closes completely but O2 valve leaks. This is the same condition as when you shut of the fuel valve first and you get a pop. The pop will be a lot quieter and in a noisy environment may not be easily heard.
ii) Condition 2: O2 valve closes completely but fuel valve leaks. When the fuel valve does not close completely, a tiny flame will appear at the tip. Look closely. The flame could be quite small. This, for obvious reasons, is a hazardous situation.
iii) Condition 3: Both valves close completely. As you would expect, when both fuel and O2 valves close completely the flame will extinguish.

Enjoy.

My answer is to follow the torch mfg's instructions for the brand of torch you may be operating at the time. I have adopted that answer from the discussion that Bill has provided a link to. It seems that depending on which brand you purchase as to how you should light and extinguish.
John Wright

edit...Well, the link seems to be down, but I do remember it created quite a debate on this forum too.

I agree with the advice to follow manfacturer's procedure.
This is how I was taught:
1) Install O2 and acetaline regulators to their respective tanks.(we'll say hoses. flame arrestors, & torch are already connected to the regulators)
2) Open up O2 tank valve all the way (we'll say you are using a cutting torch to cut-up some plate), and adjust the the regulator to 40 psi.
Note: Be sure all the valves on the torch are off before opening up the oxygen tank and keep your face away from the regulator when you oprn up the tank as typically a full O2 tank has over 2000 psi and a faulty regulator could blow apart when opening up the tank valve. Be sure tanks are secure in a cart or cutting station away from the work.
3) Open tank valve on Acetaline cylinder only enough to see pressure on the regulator( this is incase of fire that it will take less than a full rotation of the tank valve to turn it off) than adjust the outlet pressure to 7 psi. NEVER set the outlet pressure of acetaline over 15 psi as acetaline becomes unstable over this pressure.
4) There are two (2) valves for the oxygen on a cutting torch, open up the one closest to the hoses first-all the way open. Keep the other valve on the torch off until you are ready to use it.
Okay, you have your line laid out with soap stone, your plate is on a cutting table, you have a fire extinguesher near by, you have work clothes on, steel toe boots (with leather laces) and ofcourse you have been trained to make this cut. You have dark goggles(shade 5) or a dark cutting face shield. Let's go.
5) Open the O2 valve First just enough to allow a slight breeze to come out of the torch. "Crack the valve" is the term I saw used before and that works for me. Mind you that you only want a little of that 40 psi of oxygen to be flowing out of the torch.
6) Open the Acetaline torch valve (about 1/4 turn) and immediately ignite the torch with your striker keeping the torch tip away from you and anyone (or anything) near you.
You should have a whiteish flame with a slight blue stream near the tip of the torch, but be sure the flame is right at the orifices of the torch tip and not 1/4 inch or more away as someone mentioned earlier.
"We have ignition Houston."
7) Slowly and gradually open up the acetaline torch valve more (to get most of that 7 psi acetaline we set earlier) until the flame starts to jump off the torch tip, then back it off so it doesn't.
8) Gradually and slowly open up the oxygen valve until you have a neutral flame and then depress the high oxygen lever and verify you still have a neutral flame with the high oxygen applied, adjusting flow of O2 to get your neutral flame at high oxygen.

So, you have done what you had to make the cut on your plate (being glad you have a large grinder handy).

9) Turn off the Acetaline valve First, then shut off the Oxygen valve.

Note:Acetaline is the source of ignition, Oxygen supports it. Practice makes perfect and if you repeat the right things in the right sequence.....how can you go wrong???
If you have your own torch set up, you are ahead of the game because you will take good care of it. I work for a contractor with a couple of dozen cutting rigs...all with their little idiosycrencies as most are old, some have loose torch valves that change the flame output by moving too quickly, but they will get the job done safely.

This is how I was taught to use a torch by my welding instructor 20 + years ago. I will not argue other methods....this is how I do it.

Be well and be safe.