Imagine completing five, fifty-yard sprints, heck even two, and then having your head dunked in a bucket of water so that you could not catch your breath. It's not that good of a picture or thought, is it? Unfortunately, a lot of anglers don't put the connection together between the above scenario and holding a landed fish out of the water right after the fight. Keep the fish in the water while you or your buddy get the hook out and get your camera ready. I usually place the rod in between my two legs and have one hand tailing the fish and the other getting the hook out. The main point is to keep the fish in the water, because it needs to catch its breath.
Wild Bill displays excellent release practice
Another common fallacy in reviving fish, is to pull the fish back and forth through the water to help catch its breath, however most fish can only absorb dissolved oxygen one direction and not the other. This is known as countercurrent exchange, I have attached a photo of the idea behind this, but basically the water passes over the gills while the blood is flowing in the opposite direction. This allows the highest amounts of oxygen to be absorbed, however when you pull the fish backwards in the water, you are preventing this from taking place. I feel its best to just hold the fish in a soft current and let the river deliver all the oxygen the fish needs to catch its breath.
(Disclaimer: I'm not against keeping a fish, however if you plan to release it, take some pride in how you handle the fish.)