First, trout are both rather delicate and yet tougher than people think. Handling fish intelligently really isn't that hard and there are great resources out there to people that are willing to look. Handled correctly, survival rates of fish - even the more delicate trout - is very high. Under the best of conditions - small, single hooks on artificial flies and lures - catch and research mortality approaches 0%. Catch and release works - and it works better when people handle fish intelligently and respectfully.
Handling fish is not rocket surgery. Just put yourself in the position of a fish. They live in water - keeping them out of the water is like holding your head underwater. How long do you want to have your head held underwater? Not long? Me neither! They use gills to breathe, would you like somebody sticking their hands in your lungs? No? Then don't touch their gills! Ever had your head bounce off the ground? Yeah, fish don't like that either. Trout live in water and match their environment's temperature and they have a very important protective slime layer. Touching them with dry hands is poor form. Laying them on dry ground is worse. Laying them on a hot rock is especially not good for them. Would you like it if I squeezed the shit out of you? No? Neither do the fish.
It really is not more difficult than that. Treat a fish like you would like to be treated if you lived in their world.
The basic "rules" are pretty simple and they are based on science. Keep Fish Wet (https://www.keepfishwet.org/) does a really good job of highlighting the principles of handling fish, providing tips to achieve those principles, and providing the science to support their principles.
The principles are quite simple:
Minimize Air Exposure
Eliminate Contact with Dry Surfaces
Reduce Handling Time
Keep Fish Wet's principles are pretty simple, the first two in particular. Minimize air exposure and eliminate contact with dry surfaces are pretty self-explanatory and really boil down to keeping fish wet. The third one, reduce handling time, is a bit more complex because there are a lot of way to reduce handling time. Bring fish in quickly before they build up too much lactic acid, use single hooks - not treble hooks - so you can get hooks out more quickly, and if you "need" a photo, plan ahead and do it quickly and efficiently while heeding the first two principles.
As a fisheries scientist, I have handled more fish than your average person. We handle fish with a purpose and everything is organized to minimize handling time. Fish stay wet, in well oxygenated water, until they are ready to be measured, weighed, tagged, or whatever the project requires. Holding and recovery tanks are in position so fish can move from holding tank to be weighed and/or measured and placed in a recovery tank. It is all about the preparation which is a lesson for anglers. Be prepared - know what you are going to do when you catch a fish, particularly if you "need" a photograph of a fish.
A fish handling issue of growing concern is fish photography. There is no nice way I can put this - there are a ton of awful fish photos online and a number of these awful photos have resulted in more dead fish that there should be. Enough that if I were to add a 4th principle to the Keep Fish Wet list, it would be, "Think Before Taking Pictures". Or another way to put it, "Do I really need this fish photo?" and if the answer is yes, then you need to be prepared before you catch that fish. I get it, we like to show of our catches. It strokes our egos and is a way to remember our trips. If you need to get a photo and put a fish through extra handling, make it worth it. Don't take shitty outstretched arm photos - the fish deserves better. I cringe at an awful lot of Facebook and Instagram photos. So help us all and take better, more interesting fish photos and do it more safely for the fish. Please!
Kyle Zempel, owner of Black Earth Angling Co., presented to Wisconsin Trout Unlimited in their Talking Trout series about how to take better fish photographs. He provides a good number of fish handling tips as well.
Fish handling is not that difficult if you have the best interest of the fish in mind and give some thought to what their world is like. Keep Fish Wet - minimize air exposure, eliminate contact with dry surfaces, and reduce handling time. If you need that photo, get prepared before you catch the fish and mind the three principles.