I use the broomstick method when I have to put one of ours down.
Lay the hen on the ground. Place a broomstick across her neck near the base of her skull. Pull firmly on her legs until you feel her neck break. There will likely be some flopping around after her neck is broken, but it is purely reflex. I usually have a bag at the ready and place her directly in the bag, then walk away until I am sure the flopping has subsided.
Not pleasant, but it is quick and bloodless.
I'm assuming you stand on the broomstick?
Yes, stand on the broomstick. I was hastily typing that response while at work. Sorry for any confusion.