Here's a few tips I learned this season:
Get everything ready while fighting the fish. Set the camera where you expect to land the fish, turn it on and get the settings correct. Fish hate to wait.
Hold the fish with one hand while taking the picture with the other. After a few tries you should be able to do this as second nature. Getting the background level is a challenge, but again with practice it comes easier.
Shadows are a photographers enemy. If possible try to get the fish in shade, if not full sun is OK. Cloudy days make the best photos. Position yourself while taking the picture so your own shadow won't be visible.
If there is a nice backdrop use it to your advantage. Background scenery or even an old log, rock or vegetation adds much to the photo.
If there is nothing to use as a background try taking a wide shot of the fish and water.
If the fish violently protests, put it back in the water for a few seconds. If it keeps trashing let it go, you can always catch it again.
These are peeves of mine: When someone else takes your photo, hold the fish as close to your body as possible without sliming yourself. Holding the fish at arms length fools no one and looks very stupid. Do not put the rod in between your legs, throw the damn thing on the bank or in the river, the "I gotta pee" shots are some of the most embarrassing for everyone.
Now obviously I am still learning so any additional tips are welcome. A poor picture of the most beautiful fish just plain sucks.
Most of all, get out there and practice!
Let there be HIGH water!