The way to do it is the way the manufacturer directs.

Having said that... Most manufacturers direct that O2 goes off first and than fuel gas.  If you do it the reverse way it will often *pop,*  When it pops carbon is drawn down into the holes at the tip and reduces performance.

Victor, Harris and all the others ought to have web pages with specific set up, leak check, and shut down procedures for free.

If You use a gassaver valve [and those who really do a lot of starts and stops do] they turn off together and go POP, then POP again when re lit. A quick look through a Victor publication didn't give a shutdown procedure except for in the case of a flashback, where the Oxy is to be turned off first [IMMEDIATLY]. I always shut the Oxy of first and the acetylene right after and quickly as to avoid sooting up the shop.

Hello norcalwelder, as you said you have heard it both ways. Many of the publications and books will also list it both ways. I take a slightly different tact when I explain my preference for turning the torch off in a particular manner. I do suggest turning the oxygen valve off first, here's the reasoning: on a lot of torches, due to the way that they have been handled, there is the possibility of soot build-up on the seat of the fuel valve which causes it not to seal completely and leak slightly when it is shut off. Shutting the fuel off first will simply "blow out" the flame and not give any sort of indicator that the fuel valve is not completely shutting off. If you shut the torch off by shutting down the oxygen valve first and then the fuel valve, if there is any issue with the fuel valve leaking, there will be a small flame left burning. This will give you a heads up to know that you've got an issue which you need to consider if you are going to be leaving the torch laying around while you are doing something else. Either you need to have the torch valve repaired or you need to shut the fuel cylinder off when you aren't going to be using it. A lot of the time this "leaking valve" can be "fixed" by simply turning it on and off a couple of times firmly, that will re-seat the stainless steel ball on the end of the valve stem to the seat of the bottom of the valve. If that method doesn't remedy the issue you may need to disassemble the valve and clean it or possibly have it rebuilt by a qualified service person.
     The importance of paying attention to whether you have leaking fuel valves on torches goes something like this: If you are working anywhere that could be considered confined or in a hole, the acetylene gas is heavier than air and can displace air and pool in low spots or fill up confined areas. If you leave to do something else or go to lunch after turning a torch off, but don't turn the bottles off, the resulting undetected leak could possibly pool the acetylene gas and make a potential bomb. Then upon returning if you don't smell the pooled gas and have any sort of ignition source going, possibly a cigarette, you could have an explosion or fire. Just a few more thoughts for consideration. Regards, aevald