Almost seems too simple for a recipe, but here's what I do:
Peel, core and slice/dice the apples. If I'm making a large quantity, I spinkle the apple slices with a little lemon juice as I go...keeps them from browning.
Melt 1 tablespoon of butter in a large sauce pan (or 2 tablespoons in a larger stock pot if you're making a lot at once). Add sliced apples, and just a splash of lemon juice. Cook over medium heat, stirring frequently, until apples begin to mush. If you want really smooth applesauce, use a ricer or an immersion blender. (I like my applesauce kind of chunky.)
Taste test! :) If you like, add sugar. It depends on the variety of apple, but I often use a little sugar, and when I do I always use brown. If you like, add cinnamon. Sugar and cinnamon - as much or as little as you like, to taste.