Billy wants a pair of hunting dogs more than anything, but his family is too poor to buy them for him. So, he earns the money himself. Slowly. Through two years of berry-picking and rodent-trapping. The biggest thing to remember from the exposition is that for Billy, dogs = happiness.
Billy spends all his time hunting with his dogs in the woods, gleefully flinging himself into dangerous situations like near-drownings, freezing water, and skirmishes with armed hoodlums. The team overcomes one obstacle after another, even winning a gold cup and $300 at a hunting competition. They're unstoppable!
Talk about a climax: while out hunting, Billy and his dogs are attacked by a mountain lion. The dogs fight off the lion and save Billy's life, but they're wounded in the process. Seriously wounded—like, entrails dragging on the ground, wounded. It's pretty brutal.
Old Dan dies (obviously, because his insides were on his outside), and Little Ann dies from a broken heart. Needless to say, Billy is majorly, majorly depressed. His parents try to comfort him by telling him that all the money he made hunting is going to pay for them all to move to town and get educated. Shockingly, this doesn't cheer Billy up.
On the day the family is about to move, Billy visits the graves of his dogs and sees a sacred red fern growing between them. Seeing the fern gives Billy the peace he has been missing since his dogs died, and he's now ready to grow up—we mean, move to town. Happy ending? Well, not according to Hollywood. Let's call it bittersweet.