There's nothing like homemade stock. There are good commercial stocks out there, and I use them, but they never are as rich and flavorful as the stock I make myself.
I have spoken before about thrift in cooking. I save old bread, and find recipes for radish and carrot greens I would otherwise throw away. For my stock, I save the vegetable trimmings, rib bones, poultry carcasses, and ham bones.
Whenever I work with vegetables, I save the trimmings in a sealable bag in the freezer. Potato, carrot, turnip, and parsnip peels are obvious. The outer layers from onions, as well as the fibrous part of leeks and green onions adds much flavor. The ends trimmed off of celery, and whole stalks when they go rubbery, go into the bag. The woody ends of mushroom and asparagus stems are particularly good for adding richness to a stock. I like to include bell pepper trimmings as well.
I do not use trimmings from the cabbage family, including broccoli, cauliflower, and Brussels sprouts. They can add a bitter and sulphurous taste and odor. Also I only use peels from white or very pale candy cane beets. While I actually like the flavor added by red beet peels, using them turns the stock pink, which can be a visual turn-off for some people.
Many of the grocery stores in my area have deals on roasted chickens on Monday. It's not unusual for the spouse to pick one up, as it is cheaper than doing it myself, and Monday's I often don't feel like doing elaborate cooking. After removing the bulk of the meat, the carcass gets frozen. If I roast a turkey, the leftover carcass gets the same treatment. Same with the bone from a roast or a ham.
Today I'm making chicken stock. I had three chicken carcasses, and a gallon bag of vegetable trimmings. I use a large stock pot with a strainer. I put the carcasses and trimmings in the strainer, and cover with water. I let it simmer on medium low heat, occasionally adding water to keep , everything covered. I lie to let it go at least three hours, if possible, then remove the strainer. I generally leave the stock unsalted, and add salt to whatever it gets used in.
As I think I have mentioned before, I play in a Medieval and Renaissance re-creation group, the SCA. This is where I learned to value garbage stock. Some friends and I were competing in a cooking contest. The idea was that you were being besieged, and you have scrounged up the last of the food. How good a meal can you make? Well, the people running contest really didn't give us much to work with. One small turnip, a couple of small carrots, one leek, a small onion, and one chicken breast (skin on, bone in, thankfully) were typical of the quantities available. We could not afford to waste edible vegetables to make stock. So, the peels, and inedible parts, plus the chicken skin and bone, made our stock. And you know what, that stock was fabulous. It made a very solid foundation to build a number of dishes on. We ended up winning that contest, and we all felt that the stock was a significant part of that victory.
So, now I never use vegetables I could eat in a stock. I use the parts I otherwise would have thrown away, making a better use of the resources available to me. I highly recommend it.