Beef stock: Roast beef bones, onions, carrot, celery and garlic cloves in a 200 C (400 F) oven for about 40 minutes before adding to the stock pot with water, tomato paste, thyme, parsley and peppercorns. Bring to a simmer and cook for about 3 hours, skimming off the froth that rises to the top. Strain, cool and refrigerate.
Chicken stock: You can use raw chicken pieces such as backs and necks, with the skin and excess fat removed, or a chicken carcass, even a small deli chicken. Combine in stock pot with water, onion, carrot, celery, thyme, bay leaf, parsley and peppercorns and simmer for about 2 hours, skimming occasionally. Strain.
Vegetable stock: Combine cooking onions, carrots, leeks, celery, plum tomato, sun-dried tomatoes, shiitake mushrooms, garlic cloves, thyme, bay leaf and water. Simmer for 45 to 60 minutes. Strain.
Fish stock: It should be made with white fish bones, but they are hard to find. A good substitute is to use a 250-ml (1-cup) bottle of clam juice, combined with an equal amount of water and 50 ml (1/4 cup) of white wine or vermouth. If using fish heads to make stock, cut out the gills, as they can impart a bitter taste. Do not use salmon bones because they're too oily.
Do not add salt when stock is cooking because evaporation will increase the sodium content. If using commercial stock, low-sodium versions are best.
When stock has been refrigerated for several hours, remove any fat that has risen to the top before using or freezing.
Source: "Jill's Soups" by Jill Wilcox (2007).