We use the broom handle method,I have found it works better than the humane despatcher (but I am not sure I have it set right). I used it once and though wow that was quick only to find that the hen was still alive!!
There are various ways if you need to do it by hand, but the broom handle goes on a flat surface, you place the chickens head underneath, with the underside of the beak laying flat on the floor. Position the handle as close to the skull as possible, the pull up and twist at the same time, when you first do it you will either pull off the head or not do it strong enough, in which case the chicken wont be dead, go for the stronger option for the first time to stop any suffering, until you have done it once you wont be able to gauge it.
If you pick up the chicken while its alive and have a good feel at the neck and skull structure you will feel that what you are aiming to do is 'pop' the head away from the spine.
The other method I was taught is to tie up a piece of string on a beam so that when then chicken is tied upside down by its feet, the head will be just at the level of your hands when they are by your side. You then cup the head in your hands and push down and twist, this is more complicated to explain that it actually is to do it!!