Here's how to make the applesauce:
Quarter apples, removing any "icky" spots. I usually remove all of the core but I know several people who do not. Do not peel apples. Put in a big pot with an inch or so of water in the bottom. Bring to a boil, reduce heat and simmer until apples are tender and mushy, stirring occasionally so it doesn't stick/burn on bottom. Add more H2O if needed.
When apples are done (20 minutes? Half an hour? It depends on your apples and how many you have in your pot), remove from heat and let it cool a little bit. Put through a food mill - I use a Foley Food Mill like this:
I sometimes add sugar, sometimes not, depending on how sweet the apples are. Brown sugar, cinnamon, nutmeg and a pinch of salt is all nice, to taste. (You won't taste the salt, it just brings out the flavor.)
(Just Google Foley Food mill - it'll run you about $25-ish.)
If you want to can it, ladle it into clean jars and process like you would anything you are canning. I usually just let it cool and freeze it. That is, if there is any left after your kids get to it...