Yeah, it is a broad question.
Small, freestone mountain streams: Mostly small brookies but some have some browns as well. They aren't picky. For dries, parachute adams, humpies, stimulators, wulffs. Doesn't matter really, the important things are that they float high, don't waterlog, and you can see them. You are not looking for naturally rising fish here, you rarely see that. But if the water is warmer, just prospecting with dries over fishy looking water can be very effective, perhaps moreso than any other method IMO. A flashy nymph will be effective but more difficult to fish at distance, but certainly useful for early season when they won't rise to a dry real well, but typically higher water allows you to get a bit closer. Small streamers are also effective, and I tend to tie one on in those big, deep pools. I don't go for light line weights and tippets, these fish aren't line shy, or even all that drag shy. They are people shy, so the name of the game is distance. Keep low, and cast from as far away as possible. Casting in often brushy areas, and snagging plenty of trees, to me this screams a heavier, faster action fly lines and relatively short, stout 3x or 4x tippets. The longer the tippet, the better, but you have to balance it against castability in thick areas. Cover water quickly, most of these fish will hit in the first cast or two unless you spook them first. Screwing up a hole and spooking it is very common even for the best fishermen, but not to worry, there's another hole just upstream. As far as locating fish, cover is the #1 priority, which could be depth, a root system, big boulders, etc.
Larger, more fertile trout streams: Mostly brown trout, but a few have some brookies or even rainbows. The equation changes considerably. Often these fish are fairly heavily pressured. They are less people shy, but much more drag shy, so they call for longer, finer tippets and a more delicate approach. They also have their choice of many bugs and "matching the hatch" can become much more important, subsurface, surface, or "in the film." Stick with more natural looking patterns, less flash. Perhaps the most important thing is timing, in the richer streams the fish are not as opportunistic and more creatures of routine, you want to try and meet them on their schedule and match that routine. Fish the water more slowly and deliberately, they won't move as far for a fly, and they will demand that perfect drift. When the water is cold, or if it browns up a bit, streamers to the banks can be mighty effective. You can typically expect to catch fewer fish on these streams, even though more are present. But the ones you do catch will average much larger, and there's a certain satisfaction to having "figured them out." Locating fish, cover is still important, but feeding lanes go way up in importance. Eddy's where bugs collect, current breaks, near bug factory riffles, etc.
Those are the extremes, and there exists everything in between as well. In my experience, the differences between streams are larger than the differences between species. A brookie in a fertile stream will act more like any trout in a fertile stream, and a brown in an infertile freestoner will act like a fish in an infertile stream.
