The Royal Coachman is probably the most familiar brook trout fly pattern there is. Originally designed as a Coachman imitation, the red floss was wrapped around the body to make the fly more durable against the teeth of Maine brook trout.
I caught 7 brook trout on the Royal Coachman this year in a small hidden unnamed lake. A hook size #14 brought me in a 4lb brookie!
Fish the Royal Coachman like you would any other dry fly. Add a little flotant to the wings if you need to.