This is not a question most people really want the answer to. My answer is not meant to be judgmental in any way. We all do the best we can for our chameleons, and can really only follow what we personally deem to be the best advice/methods available. I have heard the "freeze them" advice very often. It seems logical and most people simply don't know that it is not as good an idea as it would seem.
What I was told, by a vet, is that chameleons can go for long periods with very shallow respiration and will live for a short time with no oxygen at all. Freezing is very painful to them. Like what "little leaf" mentioned in his post. I know of one breeder that cuts off their heads. Vet said this is not good because the cham brain will remain alive long enough to fear and suffer. I was also taught that gassing is not the best method for a chameleon (although it works well for mammals).
This is no doubt controversial, but I was taught that the most humane method is to render the chameleon unconscious first. This is best done by a vet giving an injection that is basically an overdose. It will render the cham immediately unconscious and then death follows shortly thereafter. Similar to putting down any other beloved pet.
In the absence of a vet visit, blunt force works to render the cham unconscious. One of our vets worked overseas at times, sort of a vet-without-borders, where they didn't always have access to the best pharmaceuticals. I understand that this is horrific. But the method would be to wrap the entire cham in paper or cloth, gently, lay it down on a hard flat surface. Hit the head (being careful to include the brain stem area) swift and hard with a brick or rock. This, to put it plainly, is meant to be a "crushing blow".
I am not telling anyone to do this. Fortunately, in most areas of this country we have access to vets who, although they may not be chameleon experts, do know how to put a pet down humanely.