I'm amazed how many, including seasoned, anglers take the "death grip to the line" approach after setting the hook and won't let a fish run. There's only one possible outcome when holding onto the line so LET IT RUN!! Let the fish run immediately after hooking up and ensure any loose line is clear to run freely through the guides with your hand applying the equivalent amount of drag to the line as that of your reel. Just a quick glimpse at the reel and your feet to make sure there are no potential snags ensures this. Nearly everyone has lost a trout when the line gets caught in behind the reel. It's not simply bad luck …. so make a habit of taking that quick look to ensure everything is alright.
Remember the trout is at its strongest at the moment of hookup so plan for it and act accordingly.
Once the trout settles after the first run you can actively work an angle on the fish that pulls from the fish's mouth toward its tail. Always apply pressure via the rod to the opposite way its head is pointing. Unless the trout is running they always face into the current so if you do not know which direction the head is pointing choose the downstream angle.
This is done for two reasons. Firstly, a hook that is pulled back into the side of the mouth rarely comes out as opposed to one that pulls out from an often open mouth.