Practicing catch and release is one way to help conserve the various species of fish and still be able to enjoy fishing. Unless you actually intend to cook and eat that trout you caught, there's no point in keeping it. The reason for releasing the trout (or any fish for that matter) is to help the fish survive the stress of being caught so it can continue to grow and breed.
1. Catch the trout in cold water.
Trout survive in water that's below seventy degrees Fahrenheit. Above that temperature trout are likely going to die. This is why you'll most likely find them in the cooler parts of streams, rivers or lakes in the summer. If you're serious about releasing trout to help conserve their population for future fishing, bring a thermometer along and check the water's temperature before you do any fishing. Releasing a trout in warm water is pointless as it well kill the fish anyway even if you successfully revive it.
2. Control the trout as quickly as possible.
The less stress a trout experiences during the catching, the faster it's going to revive and this makes the releasing easier. Use only barb-less hooks or flatten the barbs on the hook you'll use with pliers. Keep a slack line as maintaining constant tension is only going to make the trout fight harder perhaps to the point where it can't be revived. Some fishermen point their rods upstream parallel to the current and swing it sideways when the trout bites to quickly exert control. Afterwards you can either grab the fly (not the fish) or use a landing net. In either method, keep the trout in the water and simply and gently release the hook and let the trout swim away untouched. Tightly woven nets with rubber materials are better as it will not damage the trout's scales, fins or gills.
3. Avoid holding the trout.
Trout and other fish are covered with a protective layer of slime. Handling them with dry hands or for too long will remove this protective layer and subject the trout to fungal infection that will eventually kill it. Fish internal organs are also easily damaged so don't squeeze them or grip too tightly. If you really need to hold the trout, clasp it near the tail and turn it briefly on its side or upside down to immobilize it. Refrain from touching or putting a finger into its gills. You're most likely going to do this because you want to take a picture of it so get the camera ready beforehand to lessen the handling time.
4. Revive the trout before releasing it.
Sometimes handling the trout is unavoidable and this is the case with large sized ones as they can only be caught in the landing net after they're completely exhausted. To revive a trout hold it upright in a gentle current facing towards the current. This will get its gills working again. You'll know it has revived when it starts squirming and fighting at which point all you need to do is let go. Sometimes the trout may not revive immediately. In this case you will need to slowly move it back and forth along the water's current until it becomes active again.
Releasing a trout or any other fish after it's caught will help prevent over-harvesting. A really serious and skillful fisherman not only knows how to catch but also how to release fish. He thinks not only of the outdoor sport of fishing but also of its impact on the environment.