In Sweden, most people would brew a dark, cloudy and weak beer (1-3%) at their own farm from their own produced barley. This was stored in kegs or barrels and drunk by everyone (including young children) from wooden tankards or mugs.

Stronger beer, but still dark and cloudy, was brewed by brewers usually close to towns or bruk (early industrial sites based around copper or iron mining or work with those metals). Peasants could buy this (or make their own) for special occasions and places that served alcohol would probably be major customers. However, brännvin (vodka) was the preferred and most common way to consume alcohol at the time. The fledgling temperance movement was at the time arguing that people should restrict themselves to 6 shots of brännvin per day.

Was it commercially available? How was it sold (keg, mug, bottle) if at all? Did I brew my own? Could anyone buy at taverns?

Beer might be brewed at home or it might be produced by a commercial brewer but if you were drinking alcohol there was a very high chance that it was apple cider and there was a very high chance that it was homemade. This was the primary alcoholic drink at that time (soon the be eclipsed by spirits such as rum and whiskey).

Among the middle and upper classes a wine called madeira which is purposely oxidized and heated to extend it's life was very popular as well. Madeira was in fact the beverage used to toast the signing of the Declaration of Independence.

I know in the rural portions of United States during this time it was fairly commonplace for ciders/beers to be consumed at every meal and available in a barrel outside the house to drink from while working the farms. It was as common as water or iced tea is today and was produced in vast quantities by most rural families. The first quarter of Ken Burns' documentary on Prohibition mentions this as the norm of colonial America up until hard liquors became more popular.

You might not. Beer was still a little tough to produce at home; if you drank at home it probably would have been cider, which was much easier to brew. If you lived on a nice plot of land and were moderately wealthy you may have had a small in-house brew operation, but nothing more than your wife or maid could handle.

Source: Sarah H. Meacham, Every Home a Distillery: Alcohol, Gender, and Technology in the Colonial Chesapeake.