I vary the recipe based on what I happen to have on hand. It is a great way to clear out the vegetable bin. Tonight for example I threw in some scallions that had been forgotten in the vegetable drawer. Don't ever feel that you have to include everything listed below and certainly do not buy anything special. Although a stock pot is probably best, I often make my stock in the same large Dutch oven that I roast my chicken in (why dirty another pot).
Place the following in a pot:
all chicken bones
whatever was in the chicken during roasting (lemon, garlic, thyme)
1 tablespoon kosher salt (very important to add for flavor)
1 teaspoon peppercorns
1 head of garlic, unpeeled and cut in half crosswise
3 carrots, unpeeled and halved
3 stalks of celery, halved, with leaves
Handful of fresh parsley, thyme and/or sage
Cover with water and simmer uncovered for 4 hours. Strain, skim fat and store. Can be kept for up to one week in the refrigerator or frozen for up to 6 months.