These stoneflies hatch at night and the males are flightless which makes them any easy meal for the trout as they skitter across the water's surface. You will see the rocks on the banks littered with empty stonefly shucks from the previous nights emergence.
Tan to golden yellowish patterns that represent the adults sized in either eight or ten work best. Medium sized hopper and stonefly patterns work best. Some of my favorite patterns to use are Chubby Chernobyl's, Thunder Thighs hoppers and golden stone PMX's. You should use shorter heavy leaders from 6-7 1/2 ft with either 2x or 3x to keep your leader from twisting. Many of these patterns are buoyant enough to drop a stonefly nymph beneath to cover both the nymph and adult stages at the same time. Fishing these patterns close to the banks is the most productive and twitching the dries can elicit explosive strikes. Early mornings are best for the dry fly bite but overcast days can prolong the bite until later in the day. Fishing with a girdle bug or golden stone nymph can be productive all day long as these stoneflies nymphs are very active during this time of year.
Remember that stoneflies have incomplete metamorphism (absence of a pupal stage) which means that they crawl to the rivers bank, they split from their nymphal shuck and emerge as an adult. They have only two stages so you only need to cover either the adult or the nymph stages.
The Gallatin, Madison and Yellowstone rivers all have a significant hatch of these stoneflies but even tail waters like the Missouri river see sporadic hatch activity. It is a nice change to throw big fluffy dries on such a usually technical river.