Some rulesets ignore the matter completely. Some will tell you under what circumstances your character can drown. Some will even give a method for determining how fast he can swim. Most have magicks that will allow you to breathe under water and so not have to worry about drowning (at least, not until the magic runs out).
Here, though, is a considered analysis of how to handle aquatic activities, more or less irrespective of ruleset (although it's best for a D20 system of some kind). It's assumed that you have a rating in Constitution and in Strength, and takes it from there.
First of all, most folks are assumed to be able to swim. At least a bit. Throughout the analysis, the focus is on a 'trained' swimmer - someone who has (if the system allows) ranks in a Swimming skill. Everyone can swim a bit, though, so footnotes handle the untrained swimmers.
Next, the speed at which you swim is discussed. A trained swimmer can, at need (say, during combat) swim reasonably fast but for relatively short periods of time. Underwater movement in other settings will vary: underground or otherwise cluttered places, or when intending to swim long distance - you will not be going full pelt. This is all for unencumbered swimming - but when did you last see an adventurer in his Speedos? To deal with that, there's a table to show the effects of swimming under load.
Then comes the question of getting tired. You can walk for an hour without getting too tired, if you are in reasonable shape... but swimming for an hour is going to be noticeable. This leads on to what happens when a swimmer gets tired, covering treading water, holding your breath and... yes, drowning.
Despite disclaimers about going for playability rather than realism, this has captured most of the niceties of aquatic exploits quite well, and unless you have a troop of Navy SEALs for a party should cover at least casual waterborne activities as an addendum to your chosen ruleset.