NSFV - Not Safe For Vegetarians/Vegans
If you bake or otherwise cook whole chickens (or any other kind of bird, or really any meat with bones in it), hopefully you are already saving the carcasses and bones in the freezer. If you are not, please start doing this. One of the true joys in life is making your own soup stocks, and subsequently making amazing soups with same. I wish there was a way to share the scents of my kitchen with you right now.
You do need a stock pot. Don't think you can just use your largest regular pot and make do. Stocks are the kind of thing that it makes more sense to make large batches of and freeze, and a stock pot allows you to do just that. I currently have the carcasses of four whole chickens in my stockpot, plus some pork sausage links that I had forgotten about in my freezer.
As you can see, there is plenty of room to maneuver still :) This would have already overfilled my tallest "normal" pot. You will notice there are some large-ish chunks of meat cooking down in the stock. I don't worry about cleaning all the meat off the bone when I am cleaning up after a chicken dinner. I leave some meat on there knowing it will just make the eventual stock that much richer.
Making a soup stock is also a great way to use up vegetables that are getting old. Anything you have laying around, chop it into large chunks and toss it in the stock. In the above there is celery, onion, carrot, bell peppers and garlic. I just smash the garlic to remove the peel and toss it in without chopping it further, it will basically dissolve into the broth by the end.
Basically the point is, none of this is a precise science. Just throw what you have in your kitchen in the way of veggies into a pot with enough water to cover the carcass(es) and bones you have saved in the freezer, and simmer it down slow. Add herbs and spices to taste. One thing you definitely want to remember is to add a good amount of vinegar - it helps get all the good stuff out of the marrow in the bones. I use unfiltered raw cider vinegar because I love the taste, but any kind of vinegar works for this.
You can cook it down for a long time. I like to leave it simmering down on low heat overnight! I just strain it at the end through a colander with vertical slits (instead of holes) and freeze it in 64 oz plastic tubs that we buy yogurt in.