You should turn the jar upside down in town before it becomes smaller. Entering the library requires you to retrieve three books.

The first two books are in town. After getting the first two books, go to the mayor, and then go to the witch's house on Lake Heylia. After you enter a hole, you can get props to strengthen it and go back to town to get a third book.

After returning three books, I went to the second floor of the library to meet my elders and entered a hole. I can't remember clearly. You can take a prop and swim in the water, and then you can enter Lake Heylia.