The basics: Cook apples until they're soft. Mush them up.
That's it, really. There's several ways to cook them, and several ways to mush them up, and of course do you want to sweeten? Do you want to add other flavors? I guess I'll just make some lists of each little part here, and you can mix-and-match to your pleasure. Please do let me know how your sauce turns out!
PREP: Wash the apples. If you like the flavor and nutrients of the skin, leave it on. Keep in mind that you'll have to do more work to break it down later, unless you like large chunks of skin in your applesauce. If not, peel the apples. Unless you'll be processing the sauce through a food mill, remove the cores. (Food mills are good for many things; I've gotten two good ones at thrift stores over the years.) Cut them at least in half, to facilitate even cooking throughout.
To cook them in the oven, arrange the apples on a baking sheet or in a roasting pan or cooking pan, really any oven-proof dish big enough to hold the apples. Bake them at 350˚/180˚ until soft, as above. With oven baking, you could even just cut apples in half, core them, bake them, and scoop the flesh out of the skins.
MUSH THEM UP: Of all the adaptable steps in this "recipe", this one has the most options. Put the apples through a food mill. Or through a food processor, or a powerful blender. Or use a little elbow grease and mash them up with a hand-held utensil (potato masher, fork, rotary egg beater (the last method is untested by myself). Or put them in a big wooden tub, wash your feet, and stomp away! (This method also not tested by me.)
FLAVOR: (Or FLAVOUR, if you're a Canuck): Taste a little. Do you want it to be sweeter? (Remember, the sweetness level will "dull" a little as the sauce cools -- this is why melted ice cream tastes sweeter -- temperature does affect flavor!). Try: white sugar, brown sugar (try adding a little salt, too, for a more developed sweet note), honey, agave, or maple syrup.
Do you like the flavor? Add any of the following: cinnamon, nutmeg, ginger, cardamom (my personal fave), vanilla or other flavor extract, citrus zest, ground cloves, and/or berry jam. Other flavors to try, although you probably want to add them during the cooking stage (and pick out the remnants later): vanilla bean, cinnamon sticks, star anise, or fresh ginger.
Now, properly contain your delicious creation! Don't forget to label and date it. As you can see from the Grey Poupon jar in the first picture, I saved all my empty glass jars for several weeks before I made my applesauce and put all the fridge-bound sauce in those. You can always can it as well, using the following times: half-pints and pints @ 15 minutes, quarts @ 20 minutes.
BONUS! The easiest apple butter recipe!
Spread some applesauce on a rimmed baking sheet (AKA a jelly roll pan). Put any spices and/or sweeteners you like sprinkled over the top. I used brown sugar, a little salt, cinnamon, and ground cloves. Put in a 350˚/180˚ oven for about 30 minutes, stirring and spreading even every 10 minutes, until as thick as you like it. Store in the fridge, or water-bath can for 10 minutes. Yum! So good on English muffins.