Wash your apples.
Cut your apples into quarters. If you run into an apple with a bad spot like this one, just cut out the bad stuff and salvage what you can. You don't want to waste anything here. We need to work with "apple-volume" to get a nice pot of apple sauce. So don't let one bad spot get you started on throwing out the whole apple.
Once they are all cleaned and quartered, put them in a pot and add just enough water to get "almost" to the top of the apples. You want a few apple peeking out on top. Don't add so much water that they are completely submerged or you'll end up with apple soup. Not sauce (Although, that could be tasty if done right.).
Add 3 or 4 cinnamon sticks to the pot if it's a large one. Cut it in half if you have a smaller pot. Use your judgment here. I love cinnamon and never mind having a lot in my apple sauce. It's a decision based on personal taste.
Cook your apples on medium-high heat until they are soft. I tend to keep them boiling the whole time. But no matter what temperature you use, you need to end up with soft, mooshy sauce when you're done (apple sauce with the skins still in it.).
Put a fine meshed, sieve over a pot large enough to hold all your apple sauce (you can use a large bowl just as well).
Pour in just enough apple sauce so that when you stir it, it won't spill over the sides.
Push the sauce through the sieve as you stir until what's left is relatively dry. Scoop out, toss and repeat until you've put all your sauce through the sieve.
You now have a nice pot of apple sauce. Allow it to cool and then put it in containers and store in the fridge. You can also put some in large Ziploc bags and freeze.
For those of you who are talented in the canning department, I encourage you to do so. I've just never been very good at it. So I leave the instructions for that up to the experts.
If your apples are tart, you can stir in honey to taste.