Honestly, the first step is go where they are. It's hard to catch them where they are not. They like cold, clear, unpolluted water typically above 10,000 ft. The first and hardest step is to get where they are.
Are you looking for stream trout or lake trout, because your methods will be different for each.
Stream trout like royal wulffs up on top, and copper johns subsurface. Jigs are good too. A lot of the creeks in the Winds have a pretty steep gradient, so there's not much time for spinners to work their magic. The longer you're in the strike zone, the better chance you have. Pretty much most of the small standard high country flies will work- some better than others.
Goldens in lakes are pretty notorious for being cruisers and liking their meals deeper down. Scuds, copper johns, jigs, and lures that you let sink will probably be the ticket. A golden lake I was at recently saw most of the trout being caught with jigs. Up on the surface, they'd come within a few inches of the presentation and turn away.