Every time I make a roast chicken (which is probably 4 times a year) I save all the extra meat and the carcass, yes it's a carcass. It's dead. And this is what i do:
Throw the carcass with some of the meat still on the bones into a huge pot of water.
Add some seasonings:
1-2 tsp salt (can adjust taste after soup is done)
1 tsp pepper
1/2 tsp garlic powder
1/4 cup chopped onion
1/2 tsp chopped bay leaf
1/2 tsp parsley
sometimes random stuff like thyme, savory, whatever I feel at the moment.
Then I let it boil for few/several hours to make a nice chicken stock or broth (I still don't get the difference between a stock and broth-remind me to ask Emeril)
Occasionally I will throw in a bouillon cube.
Then after you get that nice chicken broth add:
1 large chopped potato
1/2 cup chopped carrots
1/4 cup chopped celery (with leaves)
1/4 cup peas
1/4 cup green beans
corn, other veggies you want in there. (I am guessing on measurements, I don't really measure much) or if I don't have lots of fresh veggies I'll use a bag of frozen mixed veggies. Whatever you fancy. *Add softer veggies later, like peas, beans, etc. Carrots and potatoes need the longest cooking time.
Then I adjust seasonings to taste, throw in some pasta. I prefer Ancini de pepe or little pasta stars. I usually freeze a lot, in meal size plastic ware, to thaw out one at a time for a meal here and there. It's really simple, there's not a lot to it, and you don't have to do it all at once. I put it on the stove, let it simmer, come back a few hours later, add stuff, come back later add more, etc.