Mabel.
I agree that the most 'hen friendly' outcome is to wring its neck. This may seem harsh and a little abrupt but if the hen is a pet that is probably the best course of action unless, that is, you are able to afford to spend a lot more money on the creature than can most people.
If you cannot bring yourself to do that then a farm neigbour might help but, if you have to do the job yourself; this is how I do it, but others will have their own ways of quickly despatching a laying chicken. (My heavyweight free range meat birds are different)
If you are right handed, hold the chicken in the crook of you left arm close to your body so that its wings cannot flap. Manuevre until your left hand is grasp the legs and then get the V of your index finger and thumb finger under the beak at the very top where the head and neck meet. Bend the birds head, but not neck, down in its natural forwarddirection.
You now pull the weight of the chicken down with the left hand whilst pulling up with you right hand and twisting at the same time.
You should feel, rather than hear, the neck break at the point where it supports the head. The bird will flap for a few moments.
Some people place the hen on the ground with its neck under a broom handle and then pull its legs up. If you do this make sure that the brook handle is right at the top of the neck immediately under the beak. This will ensure a quick break.
If anyone has a quicker method to despatch the occasional bird by hand, then I would be glad to change my ways.