All you need, for the way you want to do it, is a couple of ropes and a place to hang the chicken by its feet. Could be a tree or whatever. A ladder, for instance, over a door or better a garage-door opening, would work perfectly, if you have one. It keeps the chicken clear for when it flaps its wings at the end, and gives you the space to work. I cut only one vein/artery, I described how I do it in my
first post, here.
If you lack rope and/or ladder and such, you could also hold the chicken under one arm (wrapped up in a towel if you prefer) and take its head firmly in your strong hand. Pull straight and away from the chicken, dislocating the head from the neck and breaking the veins you would otherwise cut. The blood accumulates under the skin. When you cut the skin, the blood runs out. This is probably the least fussy way all-round and the way to go if one lacks set-up or tools, or just has to butcher in their kitchen for lack of better.
This method does take a bit of practice, though. If you pull too hard, the head comes off and you have a mess where you maybe didn't want it. Not pulling hard enough, is obviously not going to do the deed but might still hurt the bird and put you in a state where you have to finish the job feeling badly.
If you have a spot where you can hang the bird by its feet, do it by cutting the veins as you intended. When it has bled out (you're holding the head anyway, only in your weak hand if you decide to follow my description and you can switch to your strong hand if you prefer), you can practice the head-pull while it's hanging there. You will know you've done it right when the head comes straight off when you cut it, without having to cut or break through a boney bit.
It does take a bit of force, so practicing on a dead bird the first time gives you an idea of just how much, without having to go all out just to be sure.