In The Red Pony, what does Billy do to help the pony breathe?
When the pony, Gabilan, is very ill, having trouble breathing and only taking air in with an unnatural whistling, hissing sound, Billy helps the pony breathe by cutting a small hole into his windpipe.
It works: even though the poor animal is bleeding from the cut, he is able to breathe through the new hole and stay alive, at least for the time being.
This emergency operation is traumatic for Jody to witness, but he disregards Billy's instructions to leave and insists on staying right there with his beloved pony. And as the story comes to a close shortly after this scene, Gabilan doesn't make it--his death is heartbreaking for Jody, and for us, the readers. This sad episode can be understood in the context of the whole novel as the first of Jody's experiences with how terrible life can be. It shapes his understanding of nature, and of life, with its bittersweet mixture of tragedy and happiness.
You can find the scene involving Billy's operation on the pony toward the end of the first of the novel's four stories. (In my version of the text, it's on page 31.)