Fish colour changes can be slow or fast. Slow changes of colour (e.g. breeding colouration) are generally under the control of hormones and are usually semi-permanent. Slow colouration changes often occur as a fish grows from a larva, through juvenile and adult phases.

In contrast, the rapid colour changes (due to stress responses) are largely under control of the nervous system although hormones may also be involved. A fish caught on hook and line may change colour as a result of stress.

Further, the colour of fishes can also vary with the seasons, between day and night and even with changes in habitat and food . Some species of Flatfishes are remarkably good at quickly changing colour to match the background.

References 

http://australianmuseum.net.au/Can-fishes-change-colour/ 

Helfman, G.S., Collette, B.B. & D.E. Facey. 1997. The Diversity of Fishes. Blackwell Science. Pp. 528. 

Wallin, M. 2002. Nature’s palette. How animals, including humans, produce colours. Bioscience explained. 1(2): 1-12. (www.bioscience-explained.org/EN1.2/pdf/paletteEN.pdf)

Long term (permanent or semi-permanent) changes are due to hormonal control, e.g., from the time a fish hatches from the egg, and undergoes larval, juvenile until adult stages. Some colors develop only upon maturity of the fish when sex hormones are present, e.g., the development of colors in the bluegill from larval to adult stages.

Short term changes are due to nervous control, e.g., the change of color patterns in the Japanese flounder (Paralichthys spp) when they move from 1 location to another. Another example is the bright colors elicited in the Siamese fighting fish when 2 of them can see each other and they are about to fight.