It's kind of like the bread: it's more of a game plan than a recipe. If you have a spaghetti insert for your stockpot, it's very helpful.
I usually start by having a whole roast chicken for dinner one night. I save the skin, bones, pan juices, and leftovers as my starting point. The next morning I take my biggest pot and put in the chicken stuff. If I need lots of broth (to share or freeze), I use my big canning pot and add a whole cut up raw chicken. Really, dark meat is best for stock, so, since I found thighs on sale for .79/lb at Superfresh, I could dump a bunch of those in instead of a chicken.
I chop up 1-4 onions depending on the size of the onions (and the pot!). I like to chop up a head of garlic, too. The big thing with onions and garlic is to put in the skins. I also go through the onion bag and put in all the extra skins.
I coarsely chop some celery - mostly the tops and ends- and I peel and chop some carrots, too.
Everything into the pot! I also add a few (5?) peppercorns and a bay leaf or two.
Add enough cold water to cover, and put it on low heat. When it starts to simmer, scum will form for about 10 minutes. Skim it off and throw it away or it will turn your broth cloudy. If you miss this step, it'll still taste good, though!
Simmer it as low as you can until an hour before dinner. Minimum time with cooked chicken leftovers would be 3 hours, with raw, 4 hours would be best. Mine usually goes closer to 6 or 7.
Scoop out most of the solids (if you have an insert, you can just lift it out!), let the dark meat cool to be cut up for soup (the white meat will be tasteless and stringy), throw away the rest. Pour the rest of the stock through a strainer.
Set aside whatever you don't need to cool and freeze. A word to the wise: don't ever put a big pot of broth in the fridge. It will cool at the exact rate to provide maximal bacterial growth. You know what we used to grow bacteria in the lab? Broth. I separate the broth into gallon ziplock bags propped in loaf pans. They freeze into nice stackable bricks.
Put tonights broth in a suitable pot (could be the same pot!).
Add fresh chopped celery and carrots (peeled carrots!) to the "tonight" pot. Now is the time to salt to taste. I like to use chicken bullion cubes instead of salt to ramp up the chicken flavor even more. Simmer 45 minutes, then add the noodles. Simmer until done, then add the chicken and maybe some chopped up parsley.
Voila! Like the bread, it takes a lot of time, but not a lot of your time. Plus your house smells great!