<<Disclaimer:  Verify this information before applying it to your situation.>>

Nine years ago, when I learned that I was gluten intolerant, I was
informed by the Celiac Society that white distilled vinegar was made
from grain, that most marketed apple cider vinegar was simply white
vinegar with flavoring, and that most vinegared products (pickles,
relishes, mustards, etc.) were also made from white vinegar.  I
decided the best route for me was to make my own vinegar.

There are a lot of recipes for homemade vinegar, some using yeast,
some using vinegar 'mothers', etc., but I didn't want to use yeast nor
did I have a mother, so I went at it the natural way.  Here's what I
did.

One fall, when apples were in season and very abundant, I went to an
apple orchard and bought baskets of them...all kinds.  For days, I
peeled apples, making the apple 'meat' into applesauce, canned pie
apples, dried apples, etc., and tossing the apple peels and cores
into a bunch of crocks.  As soon as a crock was filled with apple
cores/peelings, I would fill it with water and set it in a corner.
I think that I filled about five crocks full before I finished.

Then, I let them sit...for weeks.  Remember now that the vinegaring
process requires that one kind of organism (yeast or bacteria, I forget)
turns sugars into alcohol, then another kind of organism turns the
alcohol into acetic acid (vinegar).  Unless you have a vinegar 'mother'
you have to wait for the appropriate organisms to fall into the vat
and begin the process.  Since they are in the air at all times, this
wasn't a problem to me, but the resulting fermentation process made
my house smell like I was running an illegal applejack/alcohol ring.

Anyway, I made it through the initial fermentation process.  Once the
apple peels looked spent, I strained the vinegar-to-be and let the
resulting juice continue to ferment (throw out the peels and cores).
After that, it was simply a process of letting the vinegar age and then
topping off (by using a siphon) the pure liquid while leaving behind
the residue at the bottom of the crock.

After a while, you will find a thick scum forming on the top of the
vinegar.  This is what is known as the mother.  When I was ready to
bottle my vinegar (I used those glass gallon jugs that apple juice and
wine come in), I skimmed off the mother and siphoned off the clear
liquid, throwing away the residue.  I bottled the mother for future
use and wound up with some 6 gallons of apple cider vinegar.

A few tips:
1) Keep your eye on the vinegar over the next two years as it may continue
   to accumulate residue.  You may need to siphon off the liquid another
   time or two in order to separate it from the residue.
2) The apple cider vinegar resulting from this recipe seems to be more
   acidic than the stuff in the stores, although I haven't tested it
   with litmus paper or a pH-meter.  As such, it is probably safe
   to substitute in any pickling recipes you might want to try.
3) When your store of homemade vinegar begins to run low, you can replenish
   it by either of two methods.  1) Add a small amount of your vinegar
   to a gallon of commercial FRESH apple juice or cider (don't use
   'made from concentrate' stuff) and allow it to sit and ferment just
   like the original recipe.  2) Save the peels and cores from apples
   and go through the process again, this time adding some of your saved
   mother to provide the beasties needed for the vinegar-turning process.

I know that this process sounds tedious and like too much work, and it
is, during the first year.  My six gallons of vinegar lasted for about 8
years.  Only last year did I have to make more.