First of all, let me say that I have never made my own vinegar. But I found these directions for it in a book by Sue Robishaw called Homesteading Adventures A Guide for Doers and Dreamers.
Take your apple cores and peels from whatever apple product you may be making (applesauce, apple jelly, dried apples, or what have you) and put them into a good clean plastic bucket. If you have any other fruit remains such as the pulp from wine making, jelly making, or what-not, put them into the bucket as well. Cover the fruit "generously" with warm water and drape a cloth over the top. Vinegar yeast is naturally occuring in the air, so just set your vinegar bucket in a warmish spot and wait two to six weeks. It will be pretty obvious when it's vinegar. After it has turned to vinegar a "pinkish soft slime will form over the surface. This is the mother. You can usually gently lift/skim this off (it holds together) into a jar and save it in a cool, dark place for future use." You need to store the vinegar in a container with a plastic lid because it is an acid and will corrode metal. This is true of the mother also. And store both in a cool, dark place.
She pretty much stops there, but it is my understanding that your mother is basically your yeast for your next batch of vinegar. So you would start the process over again and add the mother to the top of the water. It would just help ensure that the vinegar yeasts are there.
Sue says that vinegar that is just from apples can vary greatly in strength. She uses the best (strongest) for pickles and salads and the worst (weakest) for cleaning.
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