Take two apples of your choice and peel them. (We used hand-sized organic apples picked from a friend's tree - unknown name/variety.)
Remove the seeds and stem, and chop them in relatively similar pieces.
Place the chopped apples in a saucepan and fill with enough water to cover just to the top. Put on your stovetop with the heat on medium. After 5 minutes there should be some slight simmering. Time an additional 6-8 minutes. When done, they should be tender enough that a fork can go through.
Strain the apples and reserve the water.
Add 1/4 cup of the reserved water to the apples and use either a hand-blender, standing blender or food processor to smooth out the apples. Applesauce will happen in an instant.
Your applesauce is done. Nothing to do here but allow it to cool to room temperature before use or putting into the fridge for later. This recipes makes approximately two cups of applesauce. The process will be the same, regardless of the end-yield you'll have based on the amount of apples you use. You can add more or less reserved water before blending, depending on your preference for thick or thin sauce. My recipe here is fairly thick and it thickens just a bit more once it has completely cooled.