After you use the apples to make an apple treat, place the cores and peels in a large jar. I use a 4-cup mason jar, but you can adjust the size of the jar according to the amount of apple scraps you're using.
Cover the scraps with water and stir in the sugar.
Place a paper towel or a piece of butter muslin on top of the jar, and secure it with a band. (A coffee filter would work as well.)
Let the mixture soak for 2 weeks at room temperature (I use the back of a cabinet shelf), and then strain out the liquid. Discard the solids, which can be composted at this point.
Return the liquid to the jar and cover it again with a paper towel or butter muslin and band. Leave it for 4 more weeks, stirring daily.
Taste the vinegar and see if it has the acidity you would like. If it does, transfer it to a covered bottle for storage. If not, leave it in the large jar for a little while longer, checking every few days. (You can use it as a household cleaner if the flavor doesn't come out how you wanted it.)