How did societies adapt to using alcohol to make water safer?

Alcohol was almost surely first produced by accident. Then people noticed its intoxicating effects. It was probably not until much later that its effects on bacteria were noticed, as these didn't become really important until the population density was high enough that infected water was problematic (a small tribe living near a stream would not have this problem, for instance).

How about using kefir for milk or water to ferment the drink. This is done for ages in the East and getting more and more popular nowadays.

Question: I've heard that there were two common methods to disinfecting water in the past: boiling water or turning it into alcohol.

I believe Beer was thought to be safer because by definition it was boiled. I know the puritans who came to the America's on the Mayflower in 1620 all drank beer rather than water on the crossing as they believed it was safer. Men women and children.

How the Mayflower prepared for its historic transatlantic voyage

Though they could collect rainwater during the journey, water was not as healthy back then as it is today, and so most people liked to take beer or ale on ships. During the two weeks the group remained in Southampton, they would have had a really good opportunity to stock up. Beer-making was a big industry in the city, and they used to make it in industrial quantities so that it could be put on the ships and used for voyages. Just near to West Quay is a place that was known as the Beer House and is now called the Duke of Wellington – and it was here that the Pilgrims would have gone to get not only beer, but also French brandy and Dutch gin.

Beer by definition is boiled.

Process of brewing beer The wort(unhusked grains-sugar sources) are collected in a vessel called a kettle, brought to a controlled boil before the hops are added.

Why does beer need to be boiled Beer needs to be boiled because the high temperatures kill harmful bacteria that could contaminate the beer. Boiling has other benefits during brewing, including enzyme control, balancing sweetness and bitterness, and eliminating smells.

I also know I.P.A. or India Pale Ale was an an extra hoppy beer which was produced for British Ships making the long 6 months passage to India. This passage required the ships to cross the equator twice and sail through the tropics. The IPA beer was created with extra hops as a preservative so the beer could stand up to the demands of such a crossing. How the India Pale Ale Got Its Name

Yes, they drank beer (and/or wine depending on the availability of the ingredients) so they'd not have to drink (as much) water.
For example http://www.thekeep.org/~kunoichi/kunoichi/themestream/egypt_alcohol.html#.UUb7yVfNhgg describes in detail ancient Egyptian beer, which has actually been reproduced from recipes found.

When one sees the fell ripened fruits fermenting on the ground or in a bowl or something, it becomes apparent after enough time that there is something about fermenting fruit which distinguishing it from "rotten" food, in that it is not really going bad but going somewhere else. After seeing birds, mammals and other animals delightedly consuming them, it doesn't take much brain power to figure out that there are certain staying and keeping qualities inherent in aging fruit materials, as opposed to rotting or decomposing. Indeed, if the weather is appropriate and environment conditions are suitable, the odor of fermenting fruit can be downright enticing. Inside the house in a clean situation, it becomes a pleasant and inviting food source. I would suggest that most cultures capable of higher than basic level cooking probably have a clear distinction between foods and liquids which have become spoiled and unsafe and fermented product. The same can be said for pickling and other microbial processes that are very easily discovered and readily taken advantage of. I don't believe many cultures have survived without ever discovering fermentation.

In Anglo-Saxon England, beer was watered down, with the most watered-down called "small beer" which was used in place of water for drinking and cooking. The phrase small beer is still used, though now it means of low priority in the sense of lacking importance.

While it is true that alcohol disinfects, it is also a poor hydration source. First beers (e.g. in Egypt) were low alcohol content, even kids could drink it, and they were mayor protein/nutrition source while being more or less germless. You can argue that this is already a hygienic use. Southern and Middle Europe wine was much more available for drinking (Greeks and Rome in Ancient times, and later all the area during middle ages), but they diluted wine with water for regular consumption. Since wine has very low nutrition value compared to beer, we can argue that diluted wine consumed in large volume in daily bases is mostly a water-substitue / refreshing drink.

I know the Germans, not understanding bacteria et. Al. Actually thought the brewing process removed "evil spirits" from water, this explains why they also sometimes used beer in masonry and foundation construction, resulting in more than a few "drunk" (leaning) buildings when too much beer was used vs. straight water.