Applesauce is simultaneously an ideal project for a novice canner and also a very bad idea for a novice canner. One the one hand, there's only one ingredient (that would be apples) and no tricky timing issues like with jam or jelly. On the other hand you need, in addition to a canning kettle and jars and such, a large pot for cooking the cored* apples, a large bowl into which the softened apples with be ground, a food mill with which to actually grind them**, another bowl for dumping the spent skins out of the food mill and another smaller pot for simmering the lids and rings. Then there are little enhancements like a corer, measuring cup and cutting board, although an argument can be made that the corer isn't strictly necessary. Applesauce also makes a mess - bits of apple get everywhere - much more so than crushing tomatoes, in my experience, and you can easily give yourself a terrible burn with the hot apple flying around.
It's the part about one ingredient that gets new canners, though, and frequently a newbie cannot restrain herself from the idea of heading out to the nearest u-pick orchard and loading up on a bushel or two***. After all, is there anyone who doesn't love applesauce? Moms give it by the ton to kids, very few people are allergic to apples, it can be used by the calorie-conscious as a substitute for any number of things in baking and a bowl of warm with a bit of cinnamon is the very essence of autumn. Plus, since commercial sauce now includes more often than not the much-dreaded high fructose corn syrup or some crazy coloring agent the DIY approach is totally rational.
The process (other than the mess and resulting dishes) is simple: Core* your apples and put them in a large pot (I did half a bushel at a time, each resulting in 10 pints) with about an inch of water. Cover and heat on high, watching closely for scorching. Scorched apples are nobody's friend. Once the apples begin to soften, lower the heat and allow to get pretty gosh darn mushy. When the apples are pretty uniformly soft - and some will have begun to fall apart - remove from heat. Position your food mill over a large bowl and grind away, scooping apples from the pot into the grinder CAREFULLY using a measuring cup. When each scoop is ground down to skins, dump into another bowl and repeat until all the apples are processed. Here, if you wish, you can add a bit of cinnamon or even some of those red hot candies but it's not at all necessary - fresh applesauce is yummy completely on its own. Ladle the sauce into prepared, sterilized jars leaving 3/4 inch of headspace, seal and process in a boiling water bath for 15 minutes (for pints) or 20 minutes (for quarts). After processing, cool on a rack or folded tea towel - any jars that didn't seal can go in the fridge for more immediate use.
That's it. It took a while and made a mess, but you've just made applesauce and are a hero in many quarters.
* I have an apple corer that removes a half-inch diameter chunk from the apple center. Some people use a fancy contraption that cores and slices the apples all at once. A colleague explained to me that she doesn't bother coring, she just slices the apples in half and cooks them, relying on the food mill to take care of seeds and such. I asked if she's ever had a problem with seeds in the apple sauce and she doesn't. As I really don't enjoy coring apples at all I may consider this approach next year.
** You don't need a food mill if you just want to make the occasional batch of sauce to, say, go with dinner or as a treat for the kids. To make a single-batch, core and peel an apple per person and slice it into a saucepan with just a bit of water. Cook them down in the same fashion as the larger batch and when uniformly soft, pour them into a bowl and smash with a fork. Add cinnamon if you like and there you have a very respectable and easy side dish to go along with pork (traditionally) or just about anything else you can imagine.
*** I use "seconds" - apples that are perfectly good but not quite as ready for their close-up - at half the price of "firsts". A bushel of seconds cost me $22.00 and resulted in 20 pints of applesauce and 6 half-pints of spiced apples, not a huge savings off of retail but a very large savings on what economists call "the intangibles". Your friendly orchardist will have signs letting you know what varieties are good for which uses. For saucing I use a combination that gives me lots of different flavors blended together. My mom likes jonamacs (I think this is what they're called) for the pinky hue they lend to the resulting product. My sauce is the more standard beige but tasty nonetheless.