It was Sosuke who saved the trapped little fish. He named the little fish Ponyo.
Ponyo became a mermaid because she licked Sosuke's blood under unexpected circumstances. She and Sosuke went through many things together.
Later Ponyo was taken home by her father, but by that time Ponyo was going to become a human being. Ponyo's mother was invited back when she had to, and only she could make everything calm.
But things are far from simple. Ponyo is a mermaid, which will bring disaster to human beings after landing. Ponyo's father and mother were trying to stop Ponyo, so the disaster hit the shore.
But Sosuke and Ponyo didn't give up. Everyone was working hard to save Ponyo. Finally Ponyo and Sosuke moved Ponyo's mother, so Ponyo was allowed to become a human being, and she was with Sosuke forever.