Place apples in clean, large glass jar such as 8-cup (2-L) Mason jar. Add distilled water, ensuring apples are submerged; check that there are a few inches headspace at top of jar. Stir in raw sugar. Cover jar with double-layer of cheesecloth; secure around jar neck with elastic band.
Store at room temperature in a dark spot. Gently stir once or twice a day (re-covering with cheesecloth each time) for about 2 weeks, or until bubbles start to form, apples are soft and there is a yeasty aroma. Strain out apples and discard. Return liquid to cleaned glass jar. Cover jar with clean cheesecloth, secure with elastic band. Return jar to dark spot for another 3 weeks, or until desired level of acidity is achieved. The longer the fermentation, the more acidity.
Strain vinegar through a cheesecloth-lined fine mesh strainer, discarding the cloudy "mother culture". Transfer vinegar to clean jars or bottles with tight, re-sealable lids. Store in cupboard or dark spot. Use as desired in vinaigrettes, marinades and as an accent to finish stews and sauces in place of wine or lemon juice.
Avoid using tap water to make vinegar. Distilled water helps facilitate the fermentation process due to its purity.