I would like to make my own Chicken Stock, any suggestions?
Note that for maximum benefit I am answering the question regarding chicken stock first and at the end have included information on other stocks such as fish and brown chicken and veal stock.

Properly made stock is made from bones only.  If you cut up your own chickens then save the backs and wing tips in the freezer and use for stock.  You might ask at your grocery store or butcher and be able to purchase backs from them if you want to make stock but don't have enough.  Chicken feet are rich in gelatin and can be added to the pot to help add body to the stock.


Place chicken backs/wing tips in a large stockpot (about a 3-4 gal. stockpot).  Cover with cold water and place on stove.  Bring to a gentle simmer for about 10 minutes.  This is known as "blanching" the bones and is done to help dissolve the blood and other loose proteins from the soft bones.  These proteins will form a gray scum on the surface.  Once the scum has formed, drain off the water disarding it in the sink.  The more clear a stock is the longer the shelflife as it's the additional proteins making a stock cloudy that also cause it to spoil much more quickly.
Return bones to the pot and cover again with cold water.  Add a sachet (cheesecloth pouch containing a couple of bay leaves, about a teaspoon of whole peppercorns, a handful of parsley stems, and 8-10 thyme branches or a teaspoon of dried thyme) that's been tied up with some string.  Bring the pot to a very gentle simmer once again and allow to simmer for about 3 hours.
After 3 hours add the mirepoix (carrots, onions, celery).  Plan on 1-2 lbs. of mirepoix (combined vegetables) per 8 lbs. of bones.  I also like to add leeks as they not only add flavor but are supposed to help in clarification of the stock.  Continue to simmer the stock for 1-2 hours.  (If you're not going to be around to add the vegetables at that time they can be added with the bones but need to be cut in large pieces to avoid cooking down and disintegrating.  I would typically start chicken and veal stock at night before leaving the restaurant and allow it to simmer overnight until the next morning.)
Strain the stock through a fine mesh strainer or several layers of cheesecloth.
Cool the stock in a metal container (another pot) in an ice bath until cool to the touch and then place in storage containers and refrigerate or freeze.
Once the stock has chilled the fat will have formed a solid layer on top of the stock. Carefully remove and either discard or use for sauteeing (such as duck or chicken fat).


Additional Notes:
The same process would be followed for white veal stock (not frequently used)

If preparing a brown stock (roasted chicken, veal, beef, lamb, duck):**
These stocks are made by first rinsing the bones and then roasting in the oven at about 400 F degrees until medium brown (think iced tea color).  

Once bones are browned, smear them with a tablespoon or two of tomato paste and roast for another 5 minutes or so.  Be careful as the concentrated sugars in the tomato paste can cause it to burn and create a bitter tasting stock.  

After bones and tomato paste have roasted, place them in the stock pot and add the mirepoix to the roasting pan, tossing to coat with the fat that has rendered out and roast the mirepoix until lightly browned.  Add the mirepoix about 2 hours before finishing the stock.  Be sure carrots are cut rather large to avoid having them disintegrate and adding a strange excessively sweet taste to the stock.

Recommended cooking times for stocks:

-Fish: 30-45 minutes.  Use lean white fish bones and heads.  Lobster/shrimp stock is made from the shells and will usually yield more flavor if first roasted.  Remove gills and eyes from fish heads to prevent clouding the stock.  Do not use carrots in mirepoix or it will color the stock an orange hue.  Use onions, celery, leeks, mushrooms, and sliced lemon.

-Chicken/Duck:  4-6 hours

-Veal/Beef/Lamb:  8-12 hours (knuckle bones of veal will have the greatest amount of gelatin since the bones haven't hardened as much as those of beef)

Stocks should not be seasoned with salt as one of the primary purposes is for them to be a "stock" item that can be used for a variety of needs: soups, sauces, rice, etc.  The salt is added to the final preparation not the stock.  If stock is salted and then used for a reduction sauce the resulting sauce will be too salty.