Billy is a cowboy type kid in the 1940's living in the desert right along the Mexico border. Billy needs to trap a wolf, a pregnant wolf in fact, which has been preying on the cattle. Billy notices that his father setting a trap has transcendental implications, and he wonders about the way humans interact with reality.
Billy's life is difficult, and often lonely, but as he comes to age in the novel, he is saved by his nobility. For instance, he does manage to catch the wolf, but instead of killing the animal, he tries to return it to its home in Mexico. He encounters the wolf again throughout the story.
On his quest, Billy meets people who elaborate their personal philosophies to Billy, so he can learn and grow along the way. He meets a Catholic who converted from Mormonism and comments on the fact that whether the two religions are the same is actually not relevant—because all stories are the same story. There's only one story.
In the second act, Billy and Boyd, his brother, are recovering horses which were stolen from their estate. This brotherhood is not friendly, and Boyd works hard to keep it that way. His angry stubborn attitude is Boyd's demise when he runs his mouth to the wrong person and finds himself with a bullet in his chest. Ultimately he survives and leaves Billy to make a life with a new, young wife.
Billy crosses the border again, for a third act. He learns that Boyd has been shot in another gunfight but did not survive. Billy now goes to Mexico to reclaim his brother's bones. When he finds the grave, he must dig his brothers remains out of the ground, but he is attacked by a band of evil men who disrespect his brother's remains and attack Billy's horse. Luckily, Billy survives, and a gypsy woman helps him care for his horse.
The last image of the novel is Billy's encounter with a wounded dog. Instead of treating the dog in the careful way he treated the wolf, he scares the dog away, and then regrets it. He chases the dog but finds that it has gone away for good. He weeps.