You could do this with just chicken and call it "chicken stock", but I had a large turkey this year for Thanksgiving, which means lots of awesome turkey bones and bits and bobs, but I also have a freezer bag full of chicken parts from the past couple months which I wanted to make use of. So it's a mix of turkey and chicken parts for the first stage.

I think the magic in getting my lovely gelatinous results this time had to do with the meat-to-water ratio. I think I just was adding too much water in the past. I have since heard the suggestion in multiple places to make sure you have a quart of water per pound of poultry. So for a typical 10 quart stock pot, keep that in mind, and load it up well with the poultry and then add water around it only as much as necessary. As it boils off, you can add hot water from an electric kettle to keep everything under water without diluting it too much further. The meat and veggies themselves release moisture as they release flavor, and we are keeping this at a very very bare simmer rather than a boil, so we're not losing a ton of volume of liquids throughout the process to evaporation in my experience.

Some people do this in a crock pot with a cover on it, which is an option as well. It keeps a nice consistent temp, and with the lid it limits evaporation. 10 hours on low if that's your speed... Now on to my recent success!


Ingredients
Turkey carcass, cooked and stripped of most of the meat
Leftover cooked turkey parts (I put in wings meat and skin and all)
Uncooked turkey and chicken backs and necks (frozen and kept until being used)
1 or 2 carrots as you like, cut into big chunks
3 stalks celery, cut into big chunks
1 yellow onion, cut into big chunks (sensing a theme?) AND/OR
1 large leek, green parts and all (see note in step 2)
3-4 garlic cloves (chop roughly, or just smash--you can throw the skins in, too if you want)
A pinch of whole peppercorns
Fresh herbs of choice (I had thyme and marjoram from my garden)

1. Throw poultry parts in to a big stock pot and cover with water. Set over high heat to start to boil.
2. Meanwhile, chop all veggies, throwing them in as you finish.  For leek, slice down center and pry apart to rinse well, then (you guessed it) cut into big chunks. Toss in herbs. Add more water to cover if needed.
3. When water begins to boil, turn down to medium-low or low, so you have the barest simmer. You don't want to agitate the ingredients any more than necessary. Just a teensy bit of bubbling on the surface is needed.
4. You can skim the scum if you like throughout the cooking process, but I never do and even The Food Lab at Serious Eats has done testing to prove it doesn't really do anything to make your stock any clearer or purer. So it's up to you. 
5. Simmer for 6-8 hours uncovered. I start mine before lunch and sometime after dinner I do the rest of the steps. I have done it as long as 12-18 hours, with good flavorful results. You can go 24 if you want, it's not unheard of. The longer you go the more you will be sure to have extracted all the gelatin from the bones, and the flavor isn't going to escape out the back door, so don't hesitate to go as long as you like/need. 
6. Take two fine mesh strainers, put a layer of paper towel or cheesecloth between and nest them one inside the other. With gloves to protect your hands from hot splashing, carefully pour through strainer into another large pot. Your stock will be beautifully free of random bits, creamy yellow.
7. Here is where Alton or any professional would tell you that you must rapidly cool the broth. Never put a hot pot of anything directly into the fridge as it will warm up your fridge to potentially dangerous levels. Some people nestle their strained stock bowl/pot into a sink full of ice. Alton also takes partially filled, frozen bottles of water and drop them into the hot stock and put them in a cooler full of ice. Be grossed out if you must, but I let mine cool on the counter for a while and then put it in the fridge. It was good enough for my grandma, it's good enough for me. So far I haven't died. *fingers crossed*
8. Move to fridge then let cool overnight. Using a spatula or thin-edged ladle or spoon, skim the fat off the surface. You can reserve this for other cooking purposes (freeze in ice cube trays, then melt over rice dishes, pastas, etc for a punch of creamy fatty chickeny goodness)

At this point I had a delightfully gelatinous concoction. Over at the James Beard Foundation, they had a simple recipe to just poach a chicken/hen in this and then restrain, skim, cool, and store. I opted to do that, but also all the other steps all over again. So what I did was:

Double Stock Recipe

1. Put cooled and skimmed stock back into stock pot on stove over high heat 
2. Put a steamer basket in this and place whole 4lb chicken on it
3. Pour in water to cover
4. Chop all veggies as above, nestle with herbs around chicken and add any more water needed to be sure all is under water
5. Bring to a boil, then again turn down to a bare simmer. Skim if you like as you go along
6. 1.5-2 hours or until chicken is cooked through, lift steamer basket with chicken in it from the stock and set aside. Serve poached and hot now, or let cool until you can touch it then pull meat from bones and store for use in a future recipe.
   6b. Yes you can potentially throw these bones into a future stock. Since you cooked them for a shorter time (~2 hours), there is possibly some collagen still left to extract. Try snapping a bone. If it snaps easily it has given up all it can so just discard them. If it is still hard or bends easily, then there is more life in them bones! Freeze and save for another stock making day.
7. Strain stock as above, cool before putting in fridge as above, skim fat, etc... and voila! A double stock to call your own!

Edited to add: if you wanna get really fancy, you can make chicken consomme, which is even MORE reduced, purified, and perfected. Here is a link directly to the James Beard recipe for taking your double stock to the next level.