Moodlymoo,
I'm sorry you need to cull. It's no fun, but sometimes necessary to prevent suffering of a bird, or for the health of the flock.
Do it where the rest of the flock cannot see, and make it as quick as possible to minimize suffering and stress.
I just culled an egglayer by the "neck-stretch" method a few weeks ago (she was an infected internal layer and a goner).
I can describe the process (WARNING-SEMI-GRAPHIC):
Hold the bird by it's feet (or have a friend hold the bird by it's feet), then with your free hand (thumb under wattles, fingers under the comb) pull down & back until you feel/hear the vertibrae crunch, which means the spinal cord is broken. (This took more physical strength than I thought it would.) The bird will twitch after the spinal cord is separated, and that's when it seems like the bird is still alive, but it is not.
Another method is the "broomstick" method which I have never done. Search here on BYC and you will find a description.
I've also heard of people using sharp garden shears to completely remove the head, which might be your surest bet to get it done quickly.
Good luck.