The problem is that the Robinson family gets shipwrecked and has to make a life for themselves on an island.
One of the first problems the family has is to survive the shipwreck. Then they have to build a house, which they do creatively in trees.
Our house was thus enclosed on three sides, for behind the great trunk protected us, while the front was left open to admit the fresh sea breeze which blew directly in. (ch 3)
The family manages to find food and stay safe and healthy, but it is not an easy life. As they are there for ten years, they develop quite a sophisticated tree house home. They even find another marooned human, Emily, and take her into their family.
Emily’s father sends a ship, and Fritz Robinson goes with her as she sails home. He brings word of the island to the mainland, and it becomes a thriving colony.