The study of fish is ichthyology, and this is what it tells us: Fish are aquatic vertebrate animals with fins instead of limbs and gills instead of lungs. They move by weaving their bodies to propel themselves through the water, guiding themselves with their fins. They breathe by taking water in through their mouths and passing it over their gills; oxygen diffuses into the gills, and carbon dioxide diffuses out. Most, but not all, fish have scales on their skin; this, coupled with slimy glandular secretions from the skin, makes them waterproof. They are often camoflauged by the markings on their skin. Most fish are cold-blooded. Most fish reproduce by spawning, that is, laying an enormous number of shelled eggs which are fertilized externally; however most sharks give birth to live young.
Fish were the earliest vertebrates on the earth and are presumed to have evolved from primitive aquatic chordates; terrestrial vertebrates in turn evolved from fishes that took to land. There are three living classes of fish: the jawless Agnatha (mostly extinct, with only lampreys and hagfishes existent today), the cartiligenous Chondrichthyes (sharks, rays, and chimaeras), and the bony Osteichthyes (all the others). (Note that invertebrates like shellfish are not true fishes, and neither are air-breathing whales.) But within these three broad classes are over 20,000 living species of fish which run the gamut of fishy possibility. They can be tiny or huge (the whale shark can be 45 ft/14 m long); they live in marine, fresh, and brackish waters all over the world at depths of a few centimetres to the bottom of the ocean. Whatever their preferred habitat, each species is adapted to its environment's temperature, water pressure, and light level. Many fishes stay in organized groups called schools, but some are solitary. They may be carnivorous, herbivorous, or omnivorous. As you can see, they are a varied lot.
Fish have the misfortune of being a popular food source for other animals, particularly humans, and so the act of catching these creatures - for food or display - is known as fishing. Fishing is an ancient livelihood that was mentioned in the Odyssey and the Bible. The leading species of fish in commercial fisheries today include anchovies, cod, haddock, whiting, herring, mackerel, as well as shellfish like lobsters, crabs, shrimps, oysters, mussels, octopus, and squid. Modern fishing might utilize lines and hooks or bait - think solitary fly fisherman standing in the river - or huge boats and modern technology - mighty trawlers dragging huge nets that encircle whole schools of fish, which are then brought aboard and frozen on the spot. But whatever the method employed, modern fisheries have in many areas of the world devastated fish stocks. Here in Canada the Atlantic cod and lobster fishery has been shut down because of the severe depletion of said animals; while this already impoverished region will have a hard time absorbing the economic impact of this closure, the fish themselves may have the harder time recovering. Fish farms probably have a better chance to succeed in the long term than culling of natural stocks, for the farms breed fish specifically for commercial purposes.
With this caution in mind, I must admit that fish are an excellent source of protein and Omega-3 fatty acids, and one of the few natural sources of vitamin D outside of sunlight. Therefore, I'm going to revisit our wee friends now in culinary terms. First, let's distinguish salt water from fresh water fish. Be aware that salt water fish like cod, flounder, and tuna often have big, thick bones, while fresh water fish like catfish, perch, and trout have many tiny bones. (Why? Because salt water provides more buoyancy, so the skeletal structure of fish in the sea can be heavier.) Fish can be lean or fatty; the former concentrates its fat in the liver and has mild and pale flesh, while the latter has oil throughout the body and a darker, heavier, more flavourful flesh. Leaner fish include sea bass, cod, trout, flounder, haddock, hake, halibut, and snapper; moderately fatty fish include barracuda, bonito, and whiting; fattier fish include eel, herring, mackerel, sturgeon, and yellowtail. As for the rest, I can do no better than point you to sneff's wonderful How to select, prepare and cook fish.