With a pair of tongs, remove large parts of bones and vegetables from the pot. You can throw the bones away, but I always let it cool off on a plate then pick off every single shred of meat and edible cartilage from the bones. I am not kidding. I may never do anything with those microscopic fibers of flesh, I may never eat it, but dammit if I don't get my $3.99/pound's worth from that turkey. The vegetables will be to the point just before becoming baby food, so you can toss them, but why?! I let them cool off, sprinkle some salt, and eat them as my reward for being so economical. However, at this point, the vegetables have very little, if any, nutritional value left in them.
Carefully pour the stock through a strainer into another large pot or bowl. Place the bowl of hot stock in another bowl that is filled with ice water to quick-cool the stock. When the ice has melted, drain some of the water, and add more ice. Do this a few times until the stock is cool enough to touch.
Ladle the cooled stock to storage containers, and refrigerate overnight to allow fat to rise to the top and solidify. After fat has solidified, remove, discard.
If you actually own a liquid fat separating device of some sort, go ahead and use it to remove the liquid turkey fat from the stock before you refrigerate.
I own a fat separator. HOWEVER, I find great joy in waiting patiently for the fat in turkey (or any animal for that matter) stock to rise to the top, cool overnight in the refrigerator, and congeal into a thick layer that seals off the top of the container, then lifting the disc of solid fat off the surface of the stock in a single smooth motion with a large spoon.
Store stock in refrigerator, or freeze and keep for up to 3 months. It might safely last longer, but it won't actually. Turkey stock that has been simmered with additional garlic, ginger, a few herbs, and salt, is a little bit of a lot of awesome on a winter night.