Add 1-2 inches of water to a large stock pot.
Wash apples. Cut out and discard any bruises or bad spots.
Quarter apples and put them in the pot (seeds, skins, and all). Cover pot and cook on medium-low until the apples are all soft. Stir apples occasionally to make sure they all cook and that none burn or stick to the bottom of the pan (I find they rarely burn in a non-stick pan, but use what you have).
When apples are all done, allow them to cool slightly. Alternately, you can allow them to cool completely and refrigerate them, and finish the process the next day.
Set up the food strainer and put two bowls under it--one for the sauce, and one for the seeds, cores, and peels.
Using a ladle, ladle apples and any juice into the top of the strainer. Turn the handle. Sauce will come out one side, and the seeds, peel, and core will come out the other!
As your bowl gets full, pour it into back into your large pot for cooking. Add sugar to taste (if desired). Cook applesauce over medium-low until it is thick enough to coat the back of a spoon. Leave the lid off to let any extra liquid evaporate. Stir occasionally to prevent sticking and burning.
To can applesauce, you'll need clean, sterile jars and a water-bath canner. You can can in whatever size works for your family. If you're making applesauce for babies, 4 oz. and half-pint jars are ideal. For my family, applesauce is best served in quart jars.
Bring applesauce to a boil, stirring to prevent sticking. Keep boiling while filling jars. Ladle hot sauce into hot jars, leaving 1/2 inch headspace. Remove air bubbles, and adjust lids. Process pints and quarts 20 minutes in a water-bath canner.
Notes: This applesauce was made from apples from the espaliered trees in my garden, but I have also made applesauce with apples that I bought at the grocery store for .50 a pound (I asked the produce manager for several 40 pound boxes). Applesauce is best made with softer apples, such as Golden Delicious, and is amazing made with Honeycrisp apples, and delicious with Gala apples. Choose your favorite, or use whatever you have available.
The great thing about using a food strainer is that it's very simple and quick. If you have apples that are bruised or starting to go bad, you can simply cut out the bad spot and throw the good parts in. If you don't have a strainer, you will need to core, peel, and chop the apples before cooking them. After they are done cooking, run the mixture through a blender, or use a potato masher to mash them.
If your applesauce was too watery, it will take longer, and your applesauce will be more brown than yellow. It is still perfectly edible. Alternately, measure and reserve 8 cups of applesauce, and use them to make and can apple butter.
If you have pears instead of apples, you can make pear sauce the same way (and use the pear sauce to make pear butter instead of apple butter).