Can fish learn anything? Yes.
I once had fish in an aquarium who learned to associate food with the sound of a feeder through classical conditioning. I noticed how my fish responded to the sound of a feeder, and how the fish searched for food as soon as I hit the button on the feeder. They responded to the sound of the feeder and not the food itself. Technically and from a behavioral perspective, that is a conditioned response to a conditioned stimulus (the feeder).
So, the fish associated the sound of the feeder with the food and reacted instinctively as if they were about to get food. They had learned the response through experience as they did not show that behavior before I had the feeder.
I later introduced new fish to the aquarium. At first, they did not show any response when I hit the button on the feeder as they had not been clasically conditioned yet. It took the new fish a couple of days to become clasically conditioned (rather quick for a fish, right?).
This small experiment is just one way of illustrating classical conditioning, a concept coined by Ivan Pavlov. Pavlov illustrated classical conditioning in his classic dog experiments (1927).
To support my findings of this experiment, one study found that gold fish can be classically conditoned (Gonzalez et al., 1962), and another study found that rainbow trouts can learn to operate a trigger to release food, which reflects operant conditioning (Landless, 1976).
Well, even a fish can learn.