Some good info so far. I'll go through how I do it.
When I butcher I keep two buckets handy. One bucket gets stuff that is fed back to the flock: fat, testicles, guts, lungs, bits they will eat. The other bucket gets the head, feathers, and bits I don't want for me or to feed the flock. That gets buried in my garden or orchard to compost in place. My garden is fenced so dogs, coyotes, or such can't get into it to dig it up. In the orchard I put wire mesh over it to keep critters from digging it up. If I time it with starting a new compost pile in the bin I sometimes toss that on the bottom and cover it with enough stuff to keep it sealed so the smell does not come out. Otherwise critters will dig it up.
I cut mine into serving pieces as I butcher. Legs, thighs, and breasts go for the table. I keep the wings, back, neck, gizzard, heart, and feet for broth. The liver goes to the dogs.
I know where the feet have been and what they have walked in. I blanch the feet which makes it easy to twist the claws off and peel them. That gets them clean enough for me. It is real easy to overcook them. I bring water to a boil and drop the feet in for about 15 seconds, then dump them in the sink. If I go much longer than that the skin is really painful to get off, it just shreds. I learned how long to cook by trial and error.
When we eat the table pieces I save the bones after the meal and freeze them. When I get a gallon freezer bag full I put them in my crock pot on low and covered in water overnight, usually 14 to 20 hours. I strain that and freeze the liquid. The old bones go to the landfill.
When it is time to make broth I put a carcass in the crock pot, add a bay leaf, a dozen peppercorns, rough chopped carrot, celery, and onion, some garlic, basil, oregano, and maybe some other herbs like parsley, thyme, or chives. I thaw that liquid I froze earlier and add that if I have some and finish covering with water. If I don't have that liquid I just use water. Again overnight in the crock pot on low for 14 to 20 hours.
I then strain that through a wire mesh colander to get the big chunks out, de-fat the liquid, and strain it through cheese cloth. That's the finished broth. I pick through the residue from those big chinks and get the meat. Be careful there can be some small bones. That cooked meat is great for tacos, chicken salad, soups, or just a sandwich.
I toss the bones, I'm done with them. But the soft stuff left is saved. I use that to bait my live traps for raccoons, skunks, and possum. Or it can bait snap traps for rats or mice.
The only thing that goes to the landfill is the bones and that is after they have been well used.