Cut the carcass up into about 6 or eight pieces and cover with water. If the chicken is raw you would normally bring it to a boil and then skim of the scum that arises, but if it is cooked just proceed. Put in an onion several stalk of celery, 3 or 4 carrots, a parsnip, salt and pepper and let it cook on a low boil for about two hours. Taste and continue if not almost done. For the last 20 minutes or even after stove is off, throw in a bunch of dill and a half bunch of parsley. You do not need to chop the herbs as you will remove them. When all is done, strain the soup two or three times ending with a cheesecloth strain. If you refrigerate the soup overnight the fat will harden at the top and you merely lift the fat off and discard.

I would just make a good chicken stock, cool it down and let it sit over night in the refrigerator. all the fat and grease will float to the top and solidify making it a snap to scoop out and discard. afterwards, you can reheat it and make a nice broth.

If your carcass has a lot of meat on it, be sure to pick it clean after the stock is made. Also, when making your stock, let your bones simmer for most of the time, and add your veggies during the last hour or so of simmering. This way, they won't be too mushy and you can use them in your soup.

I have a couple of good chicken soup recipes on this site, but its a rather lengthy process since I make my soups over a course of a day or two, but they are easily adaptable to shorter time frames.