The first time I had to put down a chicken I was very nervous/scared. Nothing will stop you from feeling nervous until it is over, but I can tell you because a chicken's body is very fragile and small compared to people/other animals, it is much easier then you think. If you have a very sharp knife (kitchen or hunting knife) it only takes 2 quick strokes of the knife at most to end the life. Use a block of wood to put the chicken down against to cut off the head. Get everything ready before you get the bird, by getting the wood block set up, the knife, and a garbage bag to put the body into. Have someone hold the chicken body, while you hold the head outstretched over the block of wood and quickly with just 2 hard/downward strokes cut the head off. It will be very quick, literally a couple seconds.  The chicken will calm down very quickly if you just hold her upside down for a moment before the cutting, then put her body down aligned to the edge of the wood block and cut quickly. Put the body in the garbage bag right away, and it will spasm around for about a minute, but the animal will be passed on already. A chickens bones/neck are very small/frail and it will be done very quickly and they do not suffer.