You probably need to specify a time period, you're asking a lot of different questions depending on when.

Carbonating booze is the result of conditioning, which is sealing the liquid into an airtight container with enough yeast and sugar to do the job. The yeast eats the sugar and makes CO2, the gas has no where to go and builds up pressure. Left in this state, the liquid carbonates.

So, you need an air tight container, at the very least. The very first beers would have been dead flat and room temperature. Even after it was possible to carbonate beer, it wasn't always served like that.

I went to a late 1800's themed brewery a few weeks back. They had a keg of each of their offerings "completely flat and room temperature, as it was served at the time". Most people chose the refrigerated and carbonated version.

I'm on mobile and unable to reference sources, but later I can bring them up. That being said, I've been a brewer for over a decade, and now work as a distiller. I have numerous books lining my wall at home.

Beer is an ancient beverage. We see beer being made from the time we first started harvesting grain. Initially beer was fermented with wild yeasts in open vats and would have been very flat and unfiltered. In Egypt they would drink it through straws that would filter out the particles of grain and yeast in the drinking pots.

The iron ringed casks probably appear around the 6th or5th century BCE. Now as mentioned, carbonation is formed by the yeast eating away the sugars in the beer. They were (and still are) waterproof and pretty air tight the beer inside remains carbonated until the cask is uncorked. Usually. If you look for it, find some cask ale. It's not as fizzy as most beer, but still carbonated.

Beer in glass bottles appear around the 17th century. The problem they had is one of over carbonation. Even today many novice home brewers will have bottles explode in their basements. Back then, before sanitation and yeast was better understood, this would have been a major issue.