Pick as much meat off of the turkey carcass as you can, and reserve for soup or turkey salad.
Place the whole turkey carcass in a large stockpot. Add large chunks of vegetables and a few whole spices and sprigs of herbs.
Fill the stock pot with cold water to cover the ingredients by about an inch.
Place the pot on the stove over medium heat. Once the water reaches a fairly active simmer, adjust the heat so the liquid bubbles gently. You do not want the stock to boil, as this will lead to too much evaporation.
Also, the proteins and fats being released from the bones can emulsify and make the stock cloudy. This will not affect the final flavor of the dish, but if you want a pretty and clear stock, make sure the stock does not boil.
As the stock simmers, a layer of grayish protein foam will rise to the surface. Carefully skim this off with a large spoon or a ladle.
Let the stock simmer for several hours, adding a bit of water as necessary to maintain the volume. You should not have too much evaporation, though, if you have maintained a slow simmer.You will know when the vegetables and bones have given up all of their flavor when you can snap a small turkey bone in half with very little effort. Strain the stock through a fine strainer, pressing down on the solids. Discard the solids, and strain the stock again. If you are going to use the stock immediately, carefully skim off the fat that rises to the top. If not, you can leave the fat on as it can be more easily removed when solidified.
You will want to chill the stock very quickly. You can carefully pour the stock into a metal bowl inside a larger metal bowl that has ice in it (an ice bath) and stir until the stock has cooled.