I hang by the feet, and then holding the legs in one hand and the head in the other, I quickly and firmly dislocate the neck by pulling out and forcing the head back in that order but almost simultaneously. For a while I was afraid to try it because it seemed complicated, but then I discovered it was actually quite simple (although there is a little bit of technique to it--I encourage people who've never tried it before to try to get someone to show them first, if possible). I can't say that this is any more humane than any other good method, but I don't believe it to be any less so, and I prefer it because it is similar in effect to decapitation, but there is no blood splattering around on me or my yard and then I have a clean and intact bird to pluck, rather than working around a bloody stump of a neck--and also it requires no special equipment like a killing cone or a hatchet and chopping block, just my two hands (and a single small sharp knife to dress it afterwards)--a kettle of hot water for plucking is nice, but not even essential. And despite what some people say, the carcass DOES bleed out just fine--but the blood collects inside the skin at the top of the neck, where it congeals, and is rinsed away when the carcass is cut up during dressing.
In fact, I slaughtered a biddy just this morning this way, and the smell of the stock pot is filling the house with it's fragrance even as I write this...
My first priority is that the death be as quick and sure as possible, but beyond this I also personally appreciate a method that is as civilized and neat as possible. It makes my job more pleasant. It also is a nice touch when people might happen to wander by, as they are often pleasantly surprised and comforted to see how simple, tidy, and undramatic the process can be, which I think makes for a good impression when trying to convince people that slaughtering livestock for home use is not something weird, creepy, or gruesome, but just a normal part of life on a small farm.
As far as the "killing-cones-being-humane" debate goes, it comes to me that most of the people who seem inclined to debate one way or another as to some method being inhumane seem to tend to be the sort of people who are uncomfortable with whole idea of slaughtering an animal in the first place--regardless of method--and this editorial letter appears to be no exception. Such people's opinions are often clouded by their own inner conflicts, revulsions, and projections. IMO common sense suggests that all of the standard slaughtering methods in use (except the mechanical methods of factory farms) are pretty much equally and suitably humane when done right. It comes down to what you feel comfortable with, what you are able to take on with your skills and abilities and resources, but also, like I mentioned above, your circumstances and personal preferences of how you want to process--and possibly your cultural traditions or religious persuasion as well.
My one bit of advice to those who are looking into slaughtering but feeling ambivalent about the killing act: whatever method you use, just don't get halfway in a lose your cool--instead, see that your killing stroke is compassionate, but swift and sure--that's the best way to be humane, when all is said and done...