A very, very important point is not to let homemade the stock or broth sit around. Once it dips below 160 degrees uncovered or unrefrigerated, bacteria may form. Use an ice bath or if you are so fortunate to have an extra refrigerator in the garage to cool it down. Too hot items in the refirigerator reduce the temperature for everything else (like eggs) to spoil. Don't be scared, just be smart like the pros and have an instant food thermometer handy.
Stock: There are two types, white and brown stock. Brown stock derives its' color from roasting the chicken bones (and vegetables if desired). White stock doesn't require cooked bones. The weight baring bones(back and neck) have the most gelatin and are most desirable with wings a good option. For me, the easiest thing to do is freeze the carcase of my weekly roast chicken in zip lock bags until I have 3 to 4 pounds of bones (that's 4-5 chickens). Alternatively, I could buy 3 pounds of chicken wings or necks and make a very gelatinous white stock. A pressure cooker makes very fine brown stock extracting every ounce of flavor from the bones and speeding up the process considerably. More particular cooks than I would have a freezer of both. The white for more delicately flavored soups and sauces, the brown for a deeper flavor.
Put the chicken bones in a large stock pot with one large yellow onion, peeled and quartered, two large carrots trimmed, unpeeled and cut into 2 inch pieces, 1 fennel bulb trimmed and quartered, 2 celery stalks with leaves(the leaves have the most flavor so put in more it you have them) cut in 2 inch pieces, 2 peeled cloves of garlic, 4 stems of flat leaf Italian parsley(the stems are as important to flavor as the leaves, so don't cut them off), 2 stems fresh thyme, 1 stem rosemary, 12 whole peppercorns, 1 bay leaf, 1 tbls Kosher salt( don't try and salt the stock more than this, save that for when you use it in a recipe).
Cover to one inch with cold water ( 6-8 cups) and bring just to a boil then reduce to a gentle simmer so that just a few bubbles break the surface. Skim off any impurities and continue simmering for 4 hours. Stain through a colander lined with cheese cloth into a large bowl. Cover with plastic wrap and allow to chill over night. The next day, using a spoon peel off any solidified fat on the surface. For extra richness, return stock to clean stock pot, heat and reduce. Cool and store in quart containers then freeze. Makes 3-4 quarts.
Broth: Place a whole hen (remove giblets and liver) in a large stock pot with the same vegetables as above and cover to one inch with cold water. Some may include a parsnip, leek or garlic in the vegetable mix. Heat to almost a boil, then reduce to a simmer as if poaching. Continue to simmer for 1 hour. Remove the hen and cool. Pick the meat and use for chicken salad, casserole or soup. Save the carcase, of course. Strain the broth, chill and remove congealed fat, then reduce both as above.
Veal or beef stock is the same concept but it's not easy to get those bones piled up unless you're good friends with the butcher. Demi glace' is the next step in the line of reductions. It's generally produced by professionals as the gold standard for sauces. Consomme' is clarified stock and the process is quite advanced involving a "raft" that collects the particulate matter. The raft is made of ground meat and egg whites and cooked over low heat in the liquid. Sounds odd but it produces a clear product. I'm not an expert but I'm may give it whirl some day.