A number of fish glow naturally through a process called bioluminescence. They have a chemical called luciferin that can be caused to glow with an enzyme called luciferase. Bioluminescence is found in some deep sea fish, plankton, crustaceans and other organisms. There is a web page here at UCSB on bioluminescence:
bioluminescence UCSB .

For unnatural methods, you mention one, inserting genes from another animal to make the fish glow. These organisms are transgenic. Genes that can make the fish glow are inserted into their genome during development. I cannot think of another way to make a fish glow. However, scientists do use fluorescent tags that will glow when exposed to UV light. This is different than either natural or transgenic bioluminescence, since the energy for the chemical glow comes from an external light source instead of from within the animal.

The fluorescent tags for fish are a kind of plastic that can be injected just under the fish's skin. If the fish is caught again, it can be recognized because the injected area will glow under UV light.