If you don't already have a soup pot, you should definitely invest in one. I got mine at Ross of all places.
It doesn't get any simpler than throwing chicken, carrots, onions, celery, salt and peppercorns into a pot of water. Simmer the goodies for about an hour. I like to use chicken legs and thighs (bone in).
After cooking, allow the soup to cool. I like to put the soup in the fridge overnight to let the fat rise to the top. In the morning, skim off the layer of fat, and you have yourself a nice broth.