Well if we use one of Mr. Webster 1913's definitions:
"To deprive of life by immersion in water or other liquid."
ba's idea (which has been nuked, but went something along the lines of jamming a hose down the fish's mouth and pumping it full of water until it explodes) makes sense.

However, the more standard definition:
"To be suffocated in water or other fluid; to perish in water."
applies to fish, too.

Fish, like most forms of life, need oxygen to survive. As you may remember from biology classes, fish extract oxygen from the water as they swim by passing it over their gills. Anyone who has kept an aquarium knows that too many fish in a limited volume of water will eventually extract all the oxygen from their environment. They will begin gulping at the surface (some fish like bettas and gouramis have actually evolved the capacity to survive in this manner), and then suffocate due to lack of oxygen.

Thus, the poor fish drowns.