Brewer's yeast (Saccharomyces cerevisiae) is actually an aerobe, which means that in the presence of oxygen it will use the same process of aerobic respiration most other living organisms use. However, when you seal it up in a big airtight vat, it has no oxygen available to it, so it busts out the zymase and starts fermenting. Fermentation is less efficient than aerobic respiration, which is why the yeast only uses it when deprived of oxygen. A similar process called lactic acid fermentation occurs when muscle cells are deprived of oxygen and that's why you get muscle cramps. Just think: if you had zymase, you'd get drunk instead! Anyway, back to zymology. An important thing to know about zymase is that it's not a single enzyme but rather an enzyme complex composed of many different chemical components. Professor Arthur Harden found this out in 1929 by passing it through a very fine filter that would let small molecules through but not large ones. After being filtered, neither part would catalyze fermentation unless the two were mixed together again. This proved that fermentation required both a large molecule he called zymase proper and a small molecule he called co-zymase. This was so clever he won the Nobel Prize for it.
The summary formula for fermentation is:
C6H12O6(aq) -------------> 2C2H5OH(aq) + 2CO2(g)