Let your microwave do the work. Simply peel, core and cut apples into chunks. Put into a covered microwave dish and cook for about 10 minutes on HIGH. Check to see if it is mushy enough. Cook a couple of extra minutes if needed. (You will need to cook longer if you are using super crisp fresh apples.)
Just add a little cinnamon and nutmeg and voila, you have fresh, hot and totally wonderful applesauce. If using tart apples and you want the sauce to be sweeter, add a little brown sugar at the end. A little goes a long way.
If you want to cook the sauce on your stove, be sure to add a little water to prevent sticking to the bottom of the pan. You will also need to stir frequently to evenly cook the sauce and prevent sticking. This method works great, but the microwave method is easier and less labor and attention intensive.
Use this rule of thumb for determining quantities:
1 large apple = 3/4 cup sauce
1 medium apple = 1/2 cup sauce
1 small apple = 1/3 cup sauce
Source: NY Apple Country