Fish, as far as I know (of course there may be exceptions), don't have any vocal organs, despite the fact they are proven to be social. So how do they manage to communicate with each other? On land, organisms like the honey-bee have their "tail-wagging dance" and ants have pheromones, so what about fish?
There are a variety of fish species that produce sounds, including many species of Bocaccio (i.e. rockfish). This article is a great resource for learning more about 'fish choruses', a phenomenon where many fishes produce noise during dawn/dusk hours, much like the dawn chorus we're more familiar with for birds.
One of the most famous examples of fish vocalizations is probably the plainfin midshipman fish (listen here!). In this case, the hum is used to attract females for mating.
As for how these sounds are produced, this interview with a scientist at Scripps Institution of Oceanography says
"Fish make sounds by oscillating their swim bladder, or by rubbing the bones where their fins attach to the body, similar to how crickets make sound by rubbing their legs".
I second MZiegenhorn's answer and Xavier Mouy's comment that a variety of fish species produce sounds, and I'll shamelessly refer you to our new website FishSounds for an inventory of published research (updated up to the end of 2020 - 2021 update coming soon) on fish sound production, and some example sound clips.
Fishes don't have vocal chords, but they can produce sounds in a variety of ways. In Ingrid Katz's words: "Fishes are known to produce sounds using five mechanisms: 1) swimbladder pulsations, 2) stridulation, 3) hydrodynamic movements, 4) substrate, body and tendon vibration, 5) air release. "
Regarding yazhuo's answer about fish sound production mechanisms, you can check Eric Parmentier's work, such as for example this book chapter: Parmentier, E. and R. Diogo (2006). Evolutionary trends of swimbladder sound mechanisms in some teleost fishes. Communication in Fishes. F. Ladich, S. P. Collin, P. Moller and B. Kappor. Enfield, NH, Science Publishers: 43-68.
Now that I mention a book chapter, the entire book would be an excellent source to answer the original question, if you are up for the reading.
Fish also produce sounds; the difference is that they are put in different positions by the body to sound. The sound produced by fish is about 20Hz and therefore is difficult for humans to hear. However, these sounds can be recorded and reproduced using instruments.
Of course, some fish also rely purely on action to exchange sounds. Some fish use ultrasonic communication, similar to dolphins (although dolphins are not fish).
Some fish transfer information by changing body colour. These fish are usually located in the tropical shallow water. Some fish pass through the water with their fins flapping to communicate courtship information. A few, mostly deep-sea fish, release pheromones.