Stock is a strange dichotomy for me. It's really quite simple to make, but it makes me feel like an accomplished cook when I see water turn into a rich, golden liquid because of something I did. It might also have something to do with the fact that when I make stock, it means I have cooked with a whole chicken, which means I have cut it into pretty little pieces of drumsticks, thighs, and boneless-skinless chicken breasts. This is a somewhat complex process, so I won't get into it now. But if you'd like to make your own stock without starting with a whole chicken, I would suggest using chicken wings or chicken feet. Most supermarkets will not have these on display, but you should be able to get them if you ask the butcher. In fact, they will probably be glad to get rid of them. If you roast a whole chicken, you can also use the leftover bones for the stock. The bones from a roasted chicken will yield a slightly different result. The stock will be darker and a bit more flavorful than a stock that starts with raw bones. They both have their place in the kitchen.
When you make stock, you are infusing the water with the flavor of chicken and your choice of vegetables, yes, but mostly you are working magic with the bones. See, bones are full of collagen, and when you cook collagen slowly with a wet cooking method, the collagen dissolves and becomes gelatin. Gelatin, the thing that makes Jell-O possible, gives stock a rich, meaty mouthfeel. It's also why soup turns into goo when you put it in the refrigerator.
Basic Chicken Stock
1 chicken carcass, broken down into small pieces or 1 lb of chicken wings and/or feet (cut wings at joints, cut claws off feet)
2 carrots, cut into large chunks
2 celery stalks, cut into large chunks
1/2 onion, layers separated
Optional: herbs (1 bay leaf, a sprig of thyme, a couple sprigs of parsley, and a couple peppercorns would be what I suggest. I usually leave them out. I prefer to not risk the clash of seasonings when I put stock in a dish. Some people also put salt in their stock, but I do not. That's mostly a personal preference, but if this stock is ever going to be reduces, salting it would be a bad idea.)
1) Toss all ingredients into a large pot and pour in enough cold water to cover everything.
2) Put the pot on a burner set to medium-high, and let it come to a boil.
3) Once it has come to a boil, turn the heat down to medium-low. You want it to just be at a simmer - bubbles slowly coming to the surface.
4) Let it simmer for at least 2 hours. 4-8 hours is ideal. Check on it every once in a while to make sure it hasn't come to a boil and to remove any scum that has risen to the surface with a slotted spoon or a wire strainer.
5) When the stock is done, fill a large bowl or your sink with ice and water and place a container big enough to hold the stock in the middle. This step is not completely necessary for a batch this size, but it is reassuring from a food safety standpoint. Also, if you make a batch much larger than this, putting hot stock into your refrigerator will raise the temperature of the fridge into the "danger zone". Letting the stock cool on the stove top is also a bad idea, therefore, ice bath.
6) Place a fine strainer on top of your container, and ladle stock over the strainer into the container until the water level in the pot is low enough that you feel confident pouring the stock from the pot. You can also siphon it, but be careful not to burn yourself.
7) Stir the stock to help it cool quickly, then cover and store in the refrigerator.
8) The next day, there should be a layer of fat on the top. You should be able to just pull it off. Now your stock is done. Use it within the next few days, or freeze it for up to 3 months.