The main thing to remember about stock making, is that you want to dissolve connective tissues containing collagen into the liquid, turning these connective tissues into gelatin. The tissues that have the most collagen are silverskin membranes and cartiliage (gristle).
If you use a turkey/chicken carcass to make your stock, be sure that it didn't sit out for hours upon hours before being refrigerated or picked/simmered. Once, I got a mild case of food poisoning by using a turkey carcass that sat out to long.
I usually use precooked chicken to make chicken soup, and I always save the bones and scraps for stock. I freeze the scraps in a gallon-sized freezer bag until I need to make stock. By then, I usually have between 4 and 6 chicken carcasses.
Cooking (caramelizing) the scraps will give you a richer, deeper, color and flavor, which is one of the reasons why I like to use a precooked chicken for my soups.
I usually just use one or two large onions (with peels), and most of a bunch of celery, leaves, root end, and all. If I have some leeks, I'll use those as well. I don't normally add carrots, as I'm not terribly fond of the taste of carrots in chicken soups or sauces.
If you use raw scraps, you need to start with COLD water and the meat scraps. Bring this to a boil. As it comes up to temperature, the blood left in the meat will coagulate, and rise up to the top as a scummy foam. Skim this out as it rises up. Once it comes to a boil, and you get all the foam out, add the aromatic veggies (onions, celery, leeks if desired, etc.). This will drop the liquid below the boiling point. Add enough hot water to bring the level nearly up to the top of the pan. Bring it back to a boil, cover, and reduce to a low simmer. If you cook the stock at a hard rolling boil, you will get a cloudy stock. However, if you poach or simmer the stock, you should get a stock that is more clear. Chicken/turkey stock usually takes me about 12 hours.
For Beef stock, you want to get as much connective tissues as possible. You'll probably have to go to several butcher shops and ask for certain cuts. This is best done in the morning, before they sell out. I like to use the "knuckle" joints of shanks, as there is a lot of cartiliage on the joints. Oxtails will also yield a lot of gelatin, but they are pricey. I've also been known to save any silverskin membrane from when we peel tenderloins at work. I like to keep my eyes out when I'm shopping, as sometimes I'll find the right piece for stock. When/if I find some, I'll buy it on-the-spot, take it home, and freeze it.
Once you have all the bones/meat you need, you'll need to roast it. I cook my bones @ 350°F for about 45 minutes. I like to use a cast iron skillet (or two) for this. Once the first 45 minutes is done, I'll pull them out, add some rough-cut carrots, celery, and onions (with skins), then some tomato paste, stir it around, and back in the oven for another 45 minutes. You don't want to put a lot of bones in a skillet for this method, although, a big roasting pan works great. Once the second 45 minutes is up, take them out, place them in a stockpan, and cover with hot water (you've already cooked the blood, so you don't have to start with cold water). I like to deglaze the roasting pan(s) with some water and add that to the stockpot as well. Bring it up to a boil, cover, and reduce to a low simmer. Cook until all the cartiliage has rendered into gelatin. You'll have to pull some bones out and check them every now and then. This takes approximately 24 - 36 hours. Be prepared to either stay up all night, or sleep in shifts to eliminate the fire danger.
Fish/seafood stock is a quick one. Classically, you want to use some good scraps, like one or two fish heads, the backbone, any skin (if you're cleaning salmon, this is a good use). I usually use whatever fish scraps I can get. If you have a good fishmonger, ask them, early in the day, if they have any scraps they'd be willing to sell. I usually got mine for free, just because I was willing to wait in their shop. I usually only need a pound or two. Onions, carrots, celery, parsley stems, and leeks (if desired) are usually the aromatics added.
I like to add any shellfish shells that I have as well. Shrimp, crab, and lobster shells all work good for this.
Again, if you're using raw product, start with cold water. Skim any foam that comes up. If you use shrimp shells, you'll probably want to add the shells and veggies, then invert a plate over the shells and drop it into the pot to submerge the shells (they float straight up out of the water). You only want to cook the stock for 45 - 60 minutes, as the connective tissues in fish readily breaks down into gelatin.
Once the cartiliage has rendered off into gelatin, strain the stock, chill, and store use later use. You may freeze it if you want to, but use it within 3 months. I like to freeze my stock in ice cube trays. My stock is usually so concentrated, that one two ice cubes per cup of water will make a basic stock.
