In theory, fly-fishing is a simple sport: Pick a body of water, choose a fly-fishing rod, select your “fly” (or bait), tie a secure knot, cast your line and, hopefully, land a fish on the other end.

As we polled into the back of a creek not much wider than the skiff, our guide said you’re only going to get one shot at these fish. We turned a bend and there they were just 50 feet away, tails out ...