First, think broth. I save the necks, wings, back, feet, gizzard, and heart to make broth. If you scald the feet in pretty hot water the toe nails will twist off and you can peel the skin off. Instant clean feet.
I put all these parts plus peppercorns, carrots, celery, onion, a bay leaf, and some herbs like basil, oregano, thyme, parsley, maybe garlic, what ever I have handy and feel like using in a crock pot along with lots of water. Cook on low for maybe 10 to 12 hours. Strain the chunks out and remove the fat. I'll get maybe 5 pints of broth out of an old hen.
Then pick through the leavings and pick out the chunks of meat. Delicious cooked meat that works well in chicken salad, tacos, or casseroles. If you cook it for 12 hours it will probably have fallen off the bone. That actually makes it a bit harder to separate. I usually try for about ten hours on low.
All this comes from the stuff most people throw away. You can cook the legs, thighs, wishbone, and breasts like others have mentioned or cook them like this for maybe 7 to 8 hours.
I see that Gallorojo and I are kinda thinking alike.