If you've never fly fished I'd like to encourage you to try it out. I've always said bow hunting is cool but it's tough to get your game. Fly fishing is cool AND it really works.
To me, the toughest thing about trout fishing is trying to figure out what they're feeding on and how to present it to them. Once you figure that out, whammo, you're drilling them. Trout are unique. If they're feeding on pale morning dun and you're throwing an elk hair caddis, you won't do any good. You might as well be throwing rocks at them.
To be a good fly fisherman you have to learn how to read the bugs. You almost have to be an entomologist. You need to learn some basics and then study the river. If they're feeding on top, look and see what is floating by.
Decades ago some fly fishermen would pump their stomachs and see what they were eating but it was later determined that this was detrimental to the fish's health so I haven't seen anyone do this in a long time.
So, you need to learn to read the hatch or another option is to go to your local Bass Pro Shops and talk to someone in their fly fishing department. Tell them what river that you're going to hit and they'll tell you which flies to buy.
If you're new, what may strike you as strange is that you can't use the same fly all day long. You may be slaying them on a size 24 PMD from 8-9:30 a.m. and then suddenly the bite just stops. Dead cold. Sure, fish can quit eating but more than likely another bug is hatching and you need to switch flies.
As the years go by you'll learn the yearly patterns. For instance, in Idaho I love the stonefly hatch on the South Fork of the Boise in June. But it doesn't last forever. In Colorado they say the stonefly hatch moves upstream 1 mile a day on the Rio Grande. So different seasons will prompt different hatches/bugs. For stoneflies, look for their cases on the rocks or huge stoneflies on the brush.
I remember one year on the South Fork I saw a nice hole. I walked down to study it and a little willow was filled with stoneflies. They were crawling all over me. I pulled one off and absent mindedly flipped it out in the water. Whoa, a 24-inch rainbow slammed it. I did it again. Same result. I grabbed my fly rod and flipped out a stonefly. Wow, he snapped me off so fast it made my head spin. He looked like a bass he was so big and fat.
Then of course in late August or September everyone loves the grasshopper run. How could you not love it? Big dry flies, fish slamming them, big time visual satisfaction. So don't be scared. Go to your local Bass Pro and buy a starter kit and see if you don't fall in love with it. Then if you do like it, buy a good set-up. You'll need a backup set anyway in case you break a tip in the backcountry. I bet I have at least eight fly rods.
If you're going to visit the western states on vacation this summer, grab a fly rod. It's almost a sin to use a spinning rod on trout. Catching them on a fly rod is how it was meant to be done.