To write a book summary, we explain the most central elements in the story, which would be the exposition, rising action, conflict, falling action, and resolution.
The exposition of a story refers to any background information necessary to introduce a story. Exposition is generally revealed within the first few chapters of a book and includes characters, settings, and any backstories necessary for setting up the main story. Jean George's My Side of the Mountain opens with a journal entry written by the protagonist, Sam Gribley, who remains nameless for many of the first pages of the book. Sam informs us that he is holed up in his tree home during a winter storm and further describes what his home looks like, what things he has made to furnish the home, what provisions he has, and that he "ran away from home eight months ago to live on the land" (p. 4). We further learn that he is living on his Great-grandfather Gribley's dilapidated farm in the Catskill Mountains, has come from New York City, and has a family of eleven that includes eight siblings besides himself. We further learn that his father granted him permission to find and live off his great-grandfather's farm, saying that every boy needs an adventure, but also expected him to give up by morning. These are the sorts of exposition details you want to explain in the beginning of your summary.
It's next important to identify the conflict in the story because all action to summarize in a story revolves around the conflict. The conflict in a story is the problem the protagonist faces. There are many minor conflicts within My Side of the Mountain, including the moment Sam's falcon Frightful is kidnapped, which he depends on for survival. However, the central conflict is Sam's struggle to survive in nature. Once the conflict is identified, it's also essential to identify the climax, which is the turning point in the story, the point when the conflict reaches is its greatest intensity and when the resolution of the story is in sight. In My Side of the Mountain, the climax begins the moment he starts investigating who took Frightful.
Other paragraphs in your summary can relay the rising action, which is all action that leads to the climax, and the falling action, which is all action that leads from the climax to the resolution. When Sam first arrived, he passed the night cold and hungry because, though he caught a fish, he couldn't figure out how to make a fire to cook it. The next morning, he discovered a man named Bill in a nearby cabin who taught him how to start a fire. Other rising action includes his taking trips to the library to learn how to survive off the land, to learn how catch and train a falcon to hunt, hollowing out his tree to build his home, gathering provisions for winter, making various friends, his family members coming to visit him, and his little sister Alice coming to stay with him and building her own house. Once Sam has Frightful back, falling action includes his family coming up to the mountain and building a house on the foundations of his great-grandfather's farmhouse, which leads to the resolution of the whole Gribley family living together again happily in the open mountain air rather than in their cramped New York City apartment.