How to make vinegar ?

Vinegar is made by two distinct biological processes, both the result of the action of harmless microorganisms (yeast and "Acetobacter") that turn sugars (carbohydrates) into acetic acid.
The first process is called alcoholic fermentation and occurs when yeasts change natural sugars to alcohol under controlled conditions. In the second process, a group of bacteria (called "Acetobacter") converts the alcohol portion to acid. This is the acetic, or acid fermentation, that forms vinegar. Proper bacteria cultures are important; timing is important; and fermentation should be carefully controlled.

In simple words, Vinegar is made from the oxidation by acetic acid bacteria of ethanol in wine, cider, beer, fermented fruit juice, or nearly any other liquid containing alcohol exposed to oxygen. Acetic acid is produced in vinegar.

Not all aerobic bacteria produce good tasting vinegar. If you want to make great vinegar, you should purchase ready made vinegar starter called a “mother” or make one properly.

Commercial vinegar is produced in two types of process that differ in speed, i.e. fast and slow fermentation processes.

The slow fermentation process is used with traditional vinegars where the process occurs naturally over weeks to months.

The longer fermentation period allows for the accumulation of a nontoxic slime composed of acetic acid bacteria and soluble cellulose, known as the mother of vinegar.

Mother of vinegar has unappetizing appearance but some people still consume it and it can be found in stores. Free-living creatures that feed on the mother might exist as a part of the fermenting process; they are non-parasitic nematodes called vinegar eels.
Manufacturers still filter them out of the product before bottling although they don’t show any harm to humans.

The fast fermentation process takes only hours to days (ranges from 20 hours to 3 days). Mother of vinegar containing the bacterial culture is added to the source liquid. Then a turbine in a Venturi pump system will add air into the liquid to promote oxygenation to speed up the fermentation process.

Is it worth it to make your own vinegar?
It depends on individuals but it is becoming more and more popular to make your own vinegar.
Good home made vinegar when made properly has a much better and more complex flavors that the store bought.
Good home made vinegar has a much better and more choice

It is also fun just to see the process of nature at work.