To wring the neck
hold the chickens feet in your left hand letting it dangle upside down. slide your right hand down the neck to just below the head and grasp the neck firmly. now jerk the head down and sharply back up while twisting at the same time.. if you do this too hard you will pull off the head.. which doesnt mean much.. but it can be upsetting...
to kill with a knife:
stretch the neck out and cut from front of the neck to the back right below the head. USE A VERY SHARP KNIFE!!!!! dull knives can tear skin and be painful and messy.. use a firm steady hand and dont stab.. slice instead.
you can also kill with a stick.. but i dont like that method so i wont mention it...
DO NOT USE:
stun guns or things like them... often doesnt kill the bird...
gas- contaminates meat..
shooting- senseless waste and hard to do...
drowning- INHUMANE...
power tools.. HUGE MESS.. and they rip and shread instead of making nice clean kills...
hope this helps..
edited to add: if you are worried about getting blood everywhere you can use the chicken cone method... which is basically a traffic cone turned upside down with the chickens head poking out of the skinny end of the cone.. from there, slicing the neck is easiest. (at least i think so) mount your cone over a lined trash bin or other blood catching receptacle and after the slice, they bleed neatly out and there is very little cleanup...
i dont know how big your chickens are that need to be put down but if they are large enough, you risk pulling their heads off while swinging them around. you have to get the perfect amount of force to pull the chickens head slightly away from the neck while twisting it at the same time.. its the same motion as the wringing of the neck i described earlier.. just a little more dramatic and pretty scary..