To cull a chicken there is always the newbie friendly beheading but that is traumatic for someone who keeps them as pets due to the random firing nerves that causes it to flap. There is also the sticking method that reduces the movement and makes the chicken brain dead.
To stick: toe the birds feet and then hang it upside down or place in a killing cone. Using a sharp knife, cut the throat at the base of the neck being sure to cut the jugular. Immediately insert the knife into the birds mouth and force it through the roof of the mouth toward the back of the head into the brain cavity and give the knife a quarter turn. The piercing of the brain causes a squawk and a convulsive flap of the feathers.