Making vinegar is a two part process, both of which use biological organisms to catalyze the reactions

Reaction 1
Turning a sugar solution into alcohol using yeast - this is called alcohol fermentation.
Reaction 2
Turning the alcohol solution into acetic acid using "Acetobacter" which are a type of bacteria. This is called acid fermentation - the stage that forms vinegar.

When wine goes 'off' it is because of acetobacter getting passed the seal and further fermenting the wine into acetic acid. When this is done on purpose you get wine vinegars :) You can also make apple cider vinegar from apple juice. Lots of different varieties depending on the original solution you use.

So, first you turn normal sugar solution into alcohol, then turn the alcohol into acetic acid. As with most biological processes the timing, quantities and temperature etc all affect the fermentation process and controlled conditions are required to produce a good result.

Picture: Vinegar barrel ~ Old ~ Greece

The earliest uses of fermentation were most likely to create alcoholic beverages such as mead, wine, and beer. These beverages may have been created as far back as 7,000 BCE in parts of the Middle East. The fermentation of foods such as milk and various vegetables probably happened sometime a few thousand years later, in both the Middle East and China. While the general principle of fermentation is the same across all of these drinks and foods, the precise methods of achieving it, and the end results, differ.

Beer is made by taking a grain, such as barley, wheat, or rye, germinating and drying it, and pulping it into a mash. This mash is then mixed with hot water, and some fermentation begins. After being further treated, the liquid is transferred to a fermentation vessel, where yeast is added to the mixture. This yeast “eats” the sugar present in the mash and converts it into carbon dioxide and alcohol. After a few weeks of fermentation and a further period of conditioning, the beer is ready to be filtered and consumed.

Wine is created using a similar method that also involves fermentation. Grapes are crushed to release the sugar-rich juices, which are then either transferred quickly away from the skins or left to rest for a time to absorb some of the flavor, tannins, and color of the skins. Yeast is then added, and the grape juice is allowed to ferment for a number of weeks, at which point it is moved to different containers and fermented at a slower rate, and eventually aged or bottled.

Pickling foods, such as cucumbers, may be accomplished by submerging the vegetable one wants to pickle in a salty water solution with vinegar added. Over time, bacteria create the lactic acid that gives the food its distinctive flavor and helps to preserve it. Other foods can be pickled simply by packing them in dry salt and allowing a natural fermentation process to occur.

Milk can also be cultured, and people have been using fermentation with dairy products for nearly 5,000 years. It is speculated that early fermented dairy, such as yogurt, was the result of a natural process of fermentation that occurred when the milk was cultured by bacteria that dwelt in skin sacks used to store dairy. Yogurt these days is made by adding a number of special bacteria, such as L. acidophilus and L. bulgaricus to milk and keeping it at the proper temperature. The bacteria begin converting the sugar in the dairy to lactic acid, eventually creating what we know as yogurt.

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Vinegar is essentially a solution of acetic acid, CH3CO2H, in water.

http://wwwchem.csustan.edu/consumer/vinegar/analysis.htm

Vinegar is made by two distinct biological processes yeast and “Acetobacter

http://www.versatilevinegar.org/faqs.html