Stock

It doesn't get more basic than this.  A good stock is handy to have in the freezer and is the key to taking a lot of recipes from "OK" to something special. 

Chicken Stock:

Anytime I cook with a whole chicken, I make a stock from whatever is left.  If I butcher it before cooking, I'll save the back and use it raw.  But even if I just roast the whole chicken, it works fine.  Pick off the meat that you can use leftover and use the rest for stock.  If you are buying chicken just for this purpose, sometimes you can find chicken backs for very, very cheap.

1 chicken carcass
1 onion, quartered (don't bother to peel or chop into tiny pieces)
1 carrot, or a handful of baby carrots
1 stalk celery
1 bay leaf
1T crushed garlic
1T sea salt

Cut the chicken up into 1" pieces, chopping the bones with big heavy scissors or a meat cleaver.  It's not the end of the world if you skip this step; it is messy and takes a few minutes.  But the bone marrow is good for you, and more of it will get into your stock if the bones are chopped up.

Put everything in the crock pot, cover with water.  Cook on low overnight.  Let cool and freeze in 1-2 cup amounts.

I usually start this after dinner, getting it started while I'm doing the dishes, and leave it until morning.

If you need it the same day, cook in a stock pot on simmer a couple of hours.  30 minutes will do in an emergency, but longer is better.

Vegetable Stock:
 Don't be afraid to chop into really large chunks.  There's no need to spend all day peeling and dicing.  5 minutes hands-on prep time, max. From the Bittman book again.

1/3 c olive oil
2 onions, quartered
4 carrots, cut into chunks
2 celery stalks, cut into chunks
1 parsnip, cut into chunks (optional)
2 potatoes, quartered
2 T crushed garlic, or 6 cloves
15-20 mushrooms, halved or sliced
Small bunch parsley
2-3 sprigs thyme
1/4 c soy sauce
10 black peppercorns
1/2 c white wine (optional)
salt & pepper

1.  Best method:  Preheat oven to 450.  Coat onion, carrots, celery, parsnip, potatoes, garlic and mushrooms with oil.  Roast until browned, about 45 minutes, stirring once or twice.
2.  Faster method:  Brown same ingredients in a skillet.
3.  Combine roasted vegetables with herbs, soy sauce, peppercorns, wine, salt & pepper and 2 quarts water in a stockpot over high heat.  Put roasting pan on another burner with 1 quart water.  Bring to a boil and scrape up any stuck food bits.  Add to stockpot.
4.  Simmer until vegetables are very soft.  Strain and adjust seasoning.