I looked on multiple websites and couldn't get clear information, because there are a lot of recipes, and none completely clarified the reasoning. Most said you have to use organic sugar, for example, which I thought was just a waste of money, for example, and many said not to add any sugar at all! Like most things in life, understanding the "why's" instead of just the "how's" is what is necessary to adapt and overcome challenges.
So here is my understanding and how I'm trying it:
1) You can use full apples (or any sweet fruit I think, just no rotten parts) cut into squares, or just scraps. You could also use store bought apple cider, but that defeats the purpose IMO. When using the fruit, it will be a lot easier if you do not smash them up, because you'll need to strain it.
2) Don't add too much water to the fruit, but enough you can stir a little. Bubbles at the top are the result of fermentation, and when fermentation is complete the fruit should sink. The reason sugar is added is to increase fermentation, and speed up the whole process. Since fruit has sugar in it, it will work without it.
3) After the fruit sinks (supposed to be about a week, maybe two), strain it out, and add some ACV with mother, which will immediately begin growing and converting the alcohol into vinegar. You can also buy the yeast I'm sure. You don't have to add mother, but it is done to speed things up, since it can take months for the right yeasts to fall out of the air into the jar (and that's another reason you must use cheese cloth rather than close the lid).
4) Taste test the vinegar after the alcohol smell goes away, which should be about a month, maybe two before it tastes strong enough.
If I'm wrong on any of these assumptions then I'll post a correction. If I'm right I should have lots of ACV in about a month. Right now it smells like alcohol, but the fruit isn't sinking.