One of my favorite cooking tips ever came from Tyler Florence, who said that most chefs save up the onion peels, onion ends, carrot tips, etc., stash them in a bag in their freezer, and use them to make chicken stock.
I have a bag of veggie scraps in my freezer, and a bag of chicken bones. Once they start taking over my freezer, I dump them in my gigantic "pasta" pot with a built-in strainer. That pot is the other chicken stock game-changer. I bought it not long after we were married, because everyone on Food Network had one, but I hate cooking pasta in it. It's perfect for this.So I have veggie scraps (they don't have to be scraps, obviously. You could just add a carrot or two, a couple of stalks of celery, an onion) and chicken bones (usually from about 3 roasted chickens). I add a bit of salt (probably 2 tablespoons or so, but it all depends on how big your pot is/how much stock you're making) and about 10 peppercorns (whole ones). I cover the whole thing with water, then slowly bring the temperature up. I used to just let it boil away for a few hours, but I've since learned that it should be just barely simmering.
*Alternatively, I've also made stock in the crock-pot before. Same method (cook on low), just cooked even longer.*
Just let it do that for a few hours, cool, strain, and stash in your freezer in ziploc bags or tupperware. Let it thaw overnight in the fridge. It's so great to have on hand at all times.