My trial and error method self taught over the last few years. Maybe not the best, but it works for me, and has caught me fish all over Colorado without having much 'insider info'. Given using known good flies:
If I am getting skunked after a while I either need to keep moving, move with more stealth, or only move upstream (working downstream can be bad or good, but mostly it just spooks the fish). If the casting, approach, and stealth isn't working, I will start flipping over rocks looking for the biggest nymphs to match.
I got schooled at a local tailwater recently, one that I was very confident arriving at; the original post made me think of that day... managed a few small ones on San Juans, but could not find the nicer fish.
If I am not super confident, or at a new river, I will check the reports with a grain of salt... I will start by flipping rocks once I get there to find some good nymphs to match. Then I use setups that cover from the surface to the bottom to find where they are feeding. Sometimes it is like 2 hours of figuring out what the trout want with only a few nibbles: fly size, fly color, depth, speed of water, presentation (rising bugs, tumbling along the bottom, or dead drift?). Then after finding the right setup it can be a fish every ten minutes! If you are getting skunked, and some guy says he just caught 15... bribe that dude into some advice!
A personal belief: most store bought flies are too flashy. Even a hares ear will have something bright and flashy. I think big smart fish know better. Try some drab natural patterns if you are getting snubbed. Use your clippers in the field to modify your flies.
As dan said, fishing for big fish, you might have to hunker down for a while until the fish become used to you standing there as part of the 'background', so cool to see the fish start drifting out of hiding after being super quiet in the same spot for a while... imagine standing like a stork, quiet but ready.
I have learned that I prefer 2 big fish all day over 30 small fish. It gets frustrating, but so does catching another 6" fingerling.
PS thanks dan for the Pike tips! I am a pike virgin, hoping to find some next spring and summer to break in my 10wt. Also hoping to find some muskie.