You'll want a pot that's about 6-8 quarts in capacity. Take all bones (even ones from everyone's plates, you'll be boiling this so don't freak about this not being sanitary), and the whole carcass, and all of the vegetables and aromatics from inside the chicken, and the neck that you saved from the giblet bag and put everything in your big pot. Cover everything with water (if you don't drink your tap water, be sure to use filtered water for this too). Toss in a few peppercorns and a bay leaf.
Slowly bring to a boil. When you've reached a boil for about a minute, lower the heat super low and let pot sit, uncovered at a low simmer for about 2 hours. You can make a light broth within an hour, or if you let it go to 3 hours or 5 hours or 8 hours, nothing bad is going to happen, you'll just have a more concentrated broth of less volume, which you can thin out with water to increase the volume. I like the flavor I get after 2 hours, strong enough to impart flavor, but not too intense. You may like to experiment on your timing and decide what concentration level you like.
When you are done simmering, use a slotted spoon to skim off any film collected on top and discard. Carefully pour contents of pot into a strainer lined with cheese cloth set inside a large bowl or another large pot.
Using a ladle, portion out broth into desired freezer-safe containers. I usually split mine between 1/2 cup containers (good for sauces) and a few 1 qt. containers (good portion for soups or risotto). Let sit on the counter to cool. When broth is cool, place in refrigerator.
When the broth is refrigerator-cold, the fat will separate to the top of the broth and can be easily spooned off and discarded. The next day, spoon off the fat and place containers in freezer. Broth will keep in fridge for a week, or a few months in the freezer. You can put the broth straight into the freezer, once cooled to room temperature, but I find that when I want to defrost the broth quickly in the microwave that separating the fat is more difficult, so that's why I do the multi stage process of counter to fridge to freezer. Also, you shouldn't put hot or warm things in the freezer, so if your broth is still a tad warm (but not hot) and it is time for bed, you can still safely put it in the fridge.
Roasted your chicken for a late dinner and have no energy that night to make stock? You have two options.
1) If you'll be making the stock the next day, throw everything, neck too, into the pot, add some ice cubes and put pot into fridge. The next day, put pot on stove, add water to cover, proceed as normal.
2) If you think it may be a few days before you have time to make stock, toss the carcass, bones, neck and veggies from inside the chicken into a large ziplock and freeze. When ready, thaw them out in the fridge completely and then proceed with the recipe.