Recently I was involved in a workshop on killing chickens. I went through the entire process from killing to dressing to cooking and eating. This is the process as was taught to me
Step One: Catch the Chicken
This part can be rather tricky. If you've never caught a chicken before, my experience is that the easiest way is to catch them off guard in the coop. Just grap the chicken by the legs and lift it off the ground holding the chicken upside down by the legs. The chicken may flap around a bit, but if you're careful, and have a good grip on the legs the chicken won't get away. The important thing to remember is not to let the chicken go, because its going to be really hard to catch it again now that its on its guard.
Step two: Kill the Chicken
There are two methods that I've seen to kill a chicken. One is to simply lie the chicken on a chopping block and cut off its head. This can be rather bloody, but its a sure way to be positive that the chicken is dead.
The second method (and the one I'm going to discuss here) is to wring the chicken's neck. If this is done correctly it's a lot less messy.
So, take your chicken by the legs (you are still holding it right?). In your other hand pull down on the neck and then bend it upward very quickly. If you've done it correctly, then you will feel a snap, and the chicken will reflexivly begin to flap its wings. At this point my great grandmother would drop the chicken and let it run around the yard until it's body finished dying.(hence the term run around like chickens with their head cut off)
If you've broken the neck, then the next step is to drain out some of the blood. Hang the chicken upside down over a bucket. Then with a sharp knife reach into the mouth slightly down the throat and cut across cutting the jugular. Be very careful not to cut through the back of the neck.
Step Three: Pluck the Chicken
This step can be quite time consuming, but it's quite simple. Hang the chicken (preferably over something to catch the feathers). It's best to begin with the larger wing feathers, and simply pull in a downward motion. Take care not to try pulling in large clumps, if you try to pull too many at a time, then you risk tearing the skin. Be sure to get all the large feathers and as many of the small ones from the areas of the chicken that you plan to eat.
After you've plucked as much as you can stand, singe off the remaining feathers. Simply hold the chicken over an open flame.
Step Four: Dressing the Chicken
This step is not for the weak of stomach.
With a sharp knife, cut around the anus. Take care not to cut the intestines. Once you've cut all the way around the anus and freed the intestines from its connecting membranes move to the head of the chicken.
At this point you'll need a heavy knife or a pair of clippers. Cut off the head at the base of the neck. Reach your hand into the chicken from the neck, and try to loosen as many of the internal organs as possible. Now simply remove the internals from the anus end. If necessary reach inside the chicken to be certain that you've removed all the insides.
Step Five: Finishing up
To finish up cut off the feet, and pull out any remaining feathers. If you so desire, now is the time to skin the chicken. Then wrap the chicken and refrigerate it as soon as possible. REMEMBER, wash the chicken thoroughly before preparing.
That's it... you have yourself a fresh chicken. Now, go find yourself a good recipe.
CapnTrippy says to avoid getting poop on everything during step 4 tie a string around the anus before trying to remove it.