Notice how dogs enjoy gnawing on bones? Ever been to a restaurant where they serve bone marrow?
Boiling bones in water draws flavor out of them. Most canned broth and stock you buy--beef stock, chicken stock, etc--is just this--water boiled with bones for hours.
Most literature I've read suggests using raw bones, but some recipes call for roasted bones--the ones I've seen most often involve roasted veal bones.
I've also made stock from roasted chicken bones. The stock does still take on flavor. It's easier to get good flavor from unused bones, though.
Additionally, I've found another pitfall. I've tried to make stock from the leftover bones of bbq'd ribs. This was not a good idea. The broth had a savory flavor, as intended. Unfortunately it also had the background taste of bbq sauce. Now, when I do make stocks, I'd consider using leftover bones, but
- there have to be enough bones leftover (otherwise I get very little stock for my time or it's weak on flavor)
- the bones can't be "tainted" by other flavors (like bbq sauce)
To answer your original question, try this:
- start with a pot of plain water
- put about 4 lb of bones in per gallon of water while it's still cold, add ~1 tsp of vinegar per gallon of water
- Once the water comes to a boil, lower the heat so that it's just simmering
- this keeps the stock from getting cloudy/white (which doesn't taste bad, just looks worse)
- leave boiling for about 6-8 hours, minimum. Longer is fine, but you won't get too much more at this point.
- turn off heat, allow stock to cool fully, strain it for the bones, refrigerate
- you can speed up this step by putting the pot in a sink full of cool water
- do NOT put a hot pot in your fridge. It will heat up the fridge significantly and just make the food in there go bad.
Use this to
- make soups
- make sauces (reduce it first)
- as a substitute for water in savory dish preparations (i.e. make rice with stock instead of water. Be creative here)
The main benefits here are flavor and nutrients, but I just do it for the flavor. Cutting bones up does improve the extraction process, but if the marrow is exposed already (most beef/veal bones will be) you're fine. If you save old bones, freeze them until you have enough. Don't bother trying to make stock with the bones from one chicken.