Wash your apples in cold water really well.
Cut apple into 1 inch(2.5cm) cubes. You can keep core if you like but seeds removed. Fill a half gallon-sized jar halfway with apple
Fill a half gallon-sized jar about 60-70 % full with apple
Dissolve sugar into a cup of water.
Pour the sugar water into the jar, then add remaining water to cover the apples. Make sure to leave at least 2-3 inches(5-7cm) of headspace from the rim of the jar as the apples will expand during fermentation process.
Cover the top of the jar with coffee filter paper or cheesecloths, then secure it with a band.
Let it sit in a dark place at room temperature. Stirring the mix once or twice a day to prevent mold from forming.
Beginning of the fermentation process, it will turn into alcohol. After 3-4 weeks later, when you see no more bubble and started to smell like a vinegar, it's time to strain out the apples.
Transfer the liquid to a glass container, cover with cloths and secure with band, leave it dark place, undisturbed for the second fermentation for another 3-4 weeks.
Taste the vinegar and see if it has the acidity you would like. If it does, decant it into a glass bottle, and you can store it at room temperature for a long time.