I've been making chicken stock for years. It's a staple in my kitchen. I tend to use a store-bought, cold, roasted chicken for my soups, and I save the scraps for stock. If I actually roast a chicken (or two these days), I'll save those scraps as well. I like using these, as they're already caramelized.
If I'm using raw poultry, I start with cold water (to coagulate the blood proteins), skim the foamy junk off the top, and when it finally comes to a boil, add the aromatic veggies, cover, and reduce to a simmer/poach. Don't "boil" the stock, as it will be cloudy.
If all of the scraps I'm using are cooked, I'll start with hot water, then bring it to a boil.
I only use onions and celery for aromatics in my chicken stock. I'm not fond of the taste of carrots with chicken (I don't put carrots in my chicken soup, either). If I have some leeks, I'll use those as well. Garlic cloves, whole, and some whole peppercorns can also be used, but I prefer to leave my stock more on the unseasoned side, as I'll season it when I use it.
I usually simmer/poach my stock for about 12 hours, to render all the cartiliage into gelatine.
I strain my stock at this point, then, in a different pan, bring it up to a boil and reduce it by about half. I do this to concentrate the stock, and make it easier to store. I usually make about 1 1/2 - 2 GALLONS of stock at a time, so storage space is at a premium.
Once my stock is reduced, I'll chill it in an ice bath in my sink. I go so far as to even place a 2-L pop bottle filled with water, then frozen, into the pan to help chill the stock. I can take 2 gallons of stock from a boil to 40 degrees F in about 30 minutes.
Once my stock is chilled, I start pouring the stock into ice cube trays and freezing it. If I have a lot, this may take a few batches of freezing to do, so I keep the stock in the refrigerator when done. Once the stock is frozen, I pop the cubes out and into a gallon ziplock bag, and store that.