If you are going to peel the apples, do this first. Then, cut out the cores and cut the apples into one to two inch pieces.
Put the apples in a pot with just enough water in the bottom to prevent them from sticking – about half an inch should be plenty. Cover and bring to a boil. Turn down the heat and simmer until the apples are very tender and starting to fall apart. (The amount of time this will take depends on how many apples you are cooking – but shouldn’t be more than 10 to 15 minutes.)
If you did not peel the apples, put them through a food mill or use the back of a wooden spoon to stir/press them through the holes of a strainer. (If you used red apples, the skins will have turned your applesauce pink!) If you peeled the apples, you can pour the cooked apples into a bowl and mash with forks, spoons or a potato masher.
Taste, and if you would like, add a little lemon juice and/or sugar and cinnamon.