Take a good photo of the fish, measure its length and girth then release it back into the water. There are taxidermists who make excellent fiberglass mounts that look better and last longer than skin mounts.
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Take a bunch of photos of the fish, because if you take only one and it’s blurred it isn’t much help. Photos as soon as the fish came out of the water are best, since they’ll show the actual colors, as well as any distinctive markings (that is, different from a typically colored example of the species). And take accurate measurements of the length and girth (though if you’re going to take the dead fish to the taxidermist these aren’t necessary.)

Generally, fish mounts these days are hollow fiberglass sculptures, so the taxidermist doesn’t need the actual fish to work with. With photos and measurements you can release (or eat) the fish and still get it mounted.

But if you’re going to get a skin mount made, keep the fish moist and be very careful not to fold or break the fins, scrape off scales, or otherwise mess it up.
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