It’s fairly common, in our modern era of extreme sports and entertainment on demand, to view any form of angling as a quaint affectation, a pastime that has passed its time. I suppose that if I had had the option at the still tender age of ten to immerse myself in the frenetic, push-button madness of video games, I would have chosen those immediate and certain pleasures over placidly drowning a worm at the local reservoir in hopes that a trout might happen upon it within the next hour or two. And my life would have been vastly poorer for it.

Angling certainly provides a respite from the stress-inducing demands of modern society. Perhaps more importantly though, it brings us out into the broader home in which we live: that of a marvelously, gloriously entwined natural world. Yes, fishing is something of an idle sport. It’s a kind of mind ramble, too, I confess. But because it requires us to interact with and try to comprehend that which is not of us, fishing is a teacher, too. If an angler is at all observant, he or she begins to understand the effect of, say, water temperature and sunlight on the behavior of fish, including their willingness to take the bait. The observant angler will note, too, those times when fish ignore all forms of sunken temptations and instead feed “on top” as aquatic insects swim from their hiding places to seek the air and mate—or upon mating, return to the water’s surface to drop their eggs and die soon thereafter. To catch fish at times like these with hook and line rather than net and dynamite, you’re going to have to angle with an imitation of a bug or other form of prey.

An imitation insect, fish, amphibian or rodent, whether crafted in the traditional manner from feather and fur, or from synthetics such as Dacron and closed-cell rubber, typically weighs very little. This presents a challenge: How the devil do you get it in front of the fish, which might be rising twenty, forty, sixty feet from where you’re standing?

Unlike a bait- or lure-fishing rig, which uses either a lead weight or the weight of a lure to attain distance and pull line from the reel, the rod of a fly fisher uses the weight of the line itself to move the bait through the air and place it where desired. This is how fly fishing distinguishes itself from other forms of angling. And this is where the fun begins.

To the initial chagrin of most men, casting a fly line is unlike throwing a ball. The fly rod acts as a lever, multiplying...