Trevj's right on with the cervical dislocation. I've killed over 6,000 chickens (yes, 6 THOUSAND... I used to work on a research farm part-time) via cervical dislocation and it's reasonably quick. Don't hold the legs, cradle the bird like you would a football - this allows you to hold the wings in so that when it begins to convulse it won't tear its pectoral muscles (what we call the "breast"). Torn meat isn't the most pleasant thing to eat, especially if you'll be waiting for a period after the kill - it bruises and gets an 'off' flavor and aroma. Other than that, he's right on with the first-and-second finger, like a "claw" which doesn't allow the head to slide through. The second pads of your first- and second finger will be gripping the base of the chicken's skull at what he'd perceive as the 3- and 9-o'clock positions. Extend the neck slowly with your relaxed bird, then pull with firm pressure. It's better to pull the head clean off than it is to underpull and cause prolonged agony. Always verify that the spinal cord is severed by "pinching" with your fingers into the dislocation site - if the cord isn't severed, pull again or sever it with finger pressure. Do this quickly and efficiently - you owe it to your bird to give it a clean death.
After the convulsion stops, cut the throat and hang the bird by the feet - or hold it upside-down if you don't have a hanging spot for it. Speed counts here if you want properly drained meat.
Next, lay the bird with the ventral face up (i.e. on its back). Feel for the end of the sternum, and pluck out about a tennis-ball sized patch of feathers at that point. Once you get good at skinning, you won't even need to do this - you can just slide in against the grain of the feathers. For a first-timer though, plucking your "nick" spot like this will help avoid unnecessary contamination of the meat.
'Nick' the skin at the base of the sternum, being very careful not to overpenetrate into the intestinal cavity. make a hole about "two fingers" wide (your first and second finger of your strong-side hand) and then put your knife down. Use your two fingers to loosen the skin around the breast meat (just put your fingers in and slide them between the skin and meat - now would be an appropriate time to make a 'virginity' joke for your troop), and then stick the two fingers of your weak-side hand in the hole as well. Take a counterpoised grip, with one hand ready to pull with two fingers towards the head and one hand ready to pull towards the cloaca ('ass').
Pull smartly and swiftly in opposite directions, and the skin should tear off the breasts reasonably completely. Often, the intestines and other "goodies" will come out with the lower-half skin. If not, don't worry about the guts for now - we'll address them in a second. Focus first on de-skinning the breast meat completely to the roots of the pectorali - both majoris and minoris. The pec major is on the outside, and the minor is proximal to the sternal ridge.
Once the top half is de-skinned, you can either remove the entire ribcage and use it as a self-supporting roast (I recommend this in the field) or you can remove the pectorali. Just run your knife along the sternum and follow the exterior of the ribcage as best you can, and you'll have a nice pec major-minor breast (times two after you lather, rinse, repeat). If you want to rip the entire ribcage off, just stick your strong hand down on to the spine - or, alternately, you can hold the wings if your hands are big enough - and pull the ribcage up with your weak hand. It might take some persuasion the first time, but you'll get used to it. If it's a "no go" then chop the ribs at the spinal roots after evisceration - evisceration is as simple as just sticking your open hand (knuckles up) into the lung cavity, riding the ribcage with your fingertips pointing towards the spine, and just "raking" everything out with your hand. Look for green fluid, which would mean the gallbladder has ruptured and you should rinse the bird if possible - or get ready for a nasty taste. Any signs of fecal matter should be dealt with as best you can, being the field. Normally that would reject a bird from a food-grade kill, but the field doesn't afford that luxury.
It's important that you know the difference between crop contents and fecal matter - crop contents will often look similar to 'poop' but are in fact just fine; the crop is a sac just upstream of the "glandular stomach" and the gizzard. No harm will come from tearing the crop when you eviscerate, so don't worry about that. After evisceration, you can just "stab" from the wing-root sides with your knife and the relatively lightweight ribs will shear quite cleanly. Voilà - chicken à la St. Louis Arch.
If you tear the ribcage up without eviscerating, often the heart will stick to the inside of the ribcage - a tasty and nutritious treat for those who can stomach the idea. Don't bother mucking about with the kidneys unless you're well-versed in anatomy, and the liver is one of the most nutritious parts (if one of the least pleasant, in my opinion) to eat in a survival situation.
The drumsticks and wings can be skinned just like anything else, so I don't imagine you'll have much difficulty there - and the feet do contain some meat if you remove the tough, leathery skin first. Do NOT cook the feet 'skin-on' as you'll regret it later.
Any more questions, feel free to PM me - I've done this many, many times and I may have omitted some steps I take for granted... hope it's at least as clear as mud!
-M
