Assuming we are talking about the United States of America before their national alcohol prohibition:

The most important element to keep in mind, regarding beer production in these times, is transportation. There was no real ice-making equipment (refrigeration), bottling practices were expensive and unreliable, and the railroads hadn't yet connected a large portion of the country.

Keeping the storage issues in mind, we can be assured that the beer a commoner would consume would be extremely regional. America witnessed an incredible influx of German immigrants in the later 1800's (due mainly to guys fleeing conscription from the German Unification wars). The Germans brought with them a brewing knowledge base that was not found in other populations. It is at this time that you found the familial beginnings of the current Beer Behemoths; Pabst, Anheuser, Busch, Schlitz, Ehret, etc. These names sound familiar? Unfortunately, the common German lagering techniques and technology were impossible to replicate on the frontier. English ale yeast was hardier than German lager strains, and survived the Atlantic voyage better. Coupled with the much warmer temperatures found in the American South and Midwest, ales were the only viable economic option.

So, we know that your early beers had a strong yeast flavor, were fuller in body, and less clear.

As for the grains involved, American farmers had access to a much wider variety of grain than was found in the old homelands. Where German and English beer was once made solely from barley (with some exceptions), American farmers now had access to other crops, such as Rye, Wheat, and Corn. Brewers were not super picky, and corn, wheat and rye could be grown cheaper than barley in many parts of America. If an expensive barley malt bill could be cut with cheaper grains, it often was.

The combination of storage/spoilage issues and grain access led to some uniquely American beer styles. The most obvious would be the "Kentucky Common Ale," which was an odd, sour, heavily adjunct (corn/wheat) based beer.

Hops grow universally well in America's range. No reversion to other herbs for bittering, for the most part. There are reports of sprucetip beers with Scandinavian settlers, or random root teas being used near the Rockies, but the common hop was the only agriculturally viable method used. That being said, the West-Coast style IPA's were still a century off; I have yet to read a historic beer recipe that involves such intense bittering. Beer was mild across the board.

Tl;Dr The beers you would find pre-prohibition would be cut with different grains and brewed warm, and typically sour. If it produced enough alcohol, it wouldn't kill you due to spoilage. If it didn't kill you, you'd buy it. Assuming you lived in an agricultural community off the train line, your beers would be murky, warm, flat, sour, and weak. Mild sour ales. And you wouldn't know any better.

I don't mean to ignore the finer beers made in urban centers on the East coast. We know that German-style Biergartens popped up through the eastern seaboard and trainlines, notably in cities such as New York, St. Louis, Chicago, etc. Here, you could find much more refined beers. As the 1900's rolled along, fine German lagers began to be produced in great quantities. From my research, it seems that these beers were still quite lacking in strength, around 3 or 4%. This is based off of political testimony from times when Prohibition began rearing its head, and brewers would make ridiculous court claims of the dozens of gallons they could consume before becoming drunk. My assumption of their near-reliability, combined with the general thriftiness found in baron monopolies, leads me to think beers of that age were much more sessionable than our current draughts.

That being said, the most approachable literature I can recommend would be the books "Bitter Brew: The Rise and Fall of Anheuser-Busch and America's Kings of Beer" and "Ambitious Brew: The Story of American Beer." Bitter Beer will give you an amazing view of American business culture through the decades, and Ambitious Brew gives great insight to the emerging beer markets of the American frontiers. Have fun, and if you have any further questions, I'll do what I can to answer!

In which country? There have been several that have undergone periods of prohibition such as the Russian Empire, Iceland, Norway, Finland, and the United States just to name a few.

You've asked about the United States, and your timing is auspicious. Just last week, the Brewers Association released its annual census and found that this year, 2015, has set a new high-water mark for the number of breweries in the United States. There are now 4,144 breweries in the U.S.

It might surprise you to learn that the previous high was set in 1873, nearly 45 years before national Prohibition. In that year, there were 4,131 U.S. breweries. By 1918, that number had fallen to about 1,000. After prohibition, almost three-quarters of pre-Prohibition breweries returned, but they were quickly winnowed. By 1950, the country was down to about 400. A decade later, it was about 250. At the industry's nadir in the early 1980s, there were only about 50 independent companies producing beer in the United States.

The spread of rapid transportation after the American Civil War, and particularly the development of the refrigerated railcar made it possible for a regional brewery to spread into a national one. Improvements in production equipment made it possible for breweries to produce enough beer to saturate the territory that transportation improvements allowed them to reach. Mass media, including the spread of national newspapers and the telegraph made widespread marketing possible. Anheuser-Busch became famous through an intense marketing and anti-competition campaign that made this picture of Custer's Last Stand the most widely known painting in America.

But you ask what folks were drinking, and from about the 1880s onward, it isn't that much different from what folks are drinking today: a lot of lager with different specialties mixed in. As J. Burnitz Bacon wrote in The American Magazine in 1882:

"The production of beer in our country, and especially of which is now called "lager beer" has reached proportions that entitle it to notice as one of our principal industries, and, from the quantity consumed, it may fairly termed the beverage the million."

The first beers brewed in the United States were ales, and these remained the preferred type right up until the 1840s. /u/grantimatter had a good mention of ciders in a comment now removed. I'm deliberately avoiding discussing ciders for the most part, as I think they're a separate category. Cider was at least on par with beer in terms of popularity during America's early years, and it likely surpassed beer in the northern states. /u/grantimatter suggests Rowan Jacobsen's *Apples of Uncommon Character and the apple section of Michael Pollan's Botany of Desire if you're interested about ciders.

In the 1840s, America changed drastically as a result of an extreme surge in immigration from Germany, Ireland and Austria-Hungary. Germans brought their beer palates with them, and these displaced the traditional English ale styles. In 1840, Bavarian immigrant John Wagner set up a brewery in Philadelphia with some of (if not the) first lager yeast brought over from Europe.

As more Germans arrived, Wagner's yeast spread in Philadelphia, and demand for lager grew. Charles Engel and Charles Wolf, two Germans, set up a lager brewery in Philadelphia that by the end of the 1840s was claiming to be the largest in America, shipping lager as far away as New Orleans ─ no small feat when railroads were just getting started.

By 1857, lagers had surpassed ales in popularity in the United States, assuming a status they still haven't surrendered.

Now, it's important to note that I'm doing a disservice to the lagers of the time by simply calling them lagers, an image that conjures up things like Budweiser and Pabst. Recipes varied from place to place, and it's sometimes difficult to tell because "corn" was sometimes used in the 19th century as a generic term for any type of grain, including wheat or barley. Beers tended to be darker and more flavorful, even if they were lagers, because the goal was to meet the needs of a smaller population rather than competing for the widest possible market.

One of the bibles of pre-Prohibition brewing is the mammoth 713-page One Hundred Years of Brewing, which was published in 1901 and covers American brewing during the 19th century in intricate detail. It was so popular that it was brought back in a new printing during the 1970s. It has plenty of passages describing the flavor and taste of different types of beer across the United States.

If you're looking for something more modern and less technical, try Maureen Ogle's Ambitious Brew, which dates from 2006 and is a pretty good attempt to create a history of American brewing. Tom Acitelli's The Audacity of Hops fills in the spots where Ogle's work falters (mainly the post WWII era), and it benefits from seven more years of perspective on the craft beer movement.