What lessons does Jess learn? Who teaches him those lessons?
I believe that the question is asking about Jess from Bridge to Terabithia. That is an emotionally difficult book to read because the lessons that Jess learns are tough life lessons.
One lesson that he learns is the value of true friendship. When Jess first meets Leslie, he is not happy about her being in his class. She beats all of the boys at their running competition, and Jess is not happy about it. But as the story continues, Jess and Leslie become the very definition of best friends. They love each other (non-romantic love), and they want the very best for each other. Deep down Jess knows this, but he doesn't realize what Leslie means to him until he loses her. When Leslie dies, Jess feels as if a part of himself has died too. By losing Leslie, Jess learned exactly how fulfilling a true friendship is.
Jess also learns a lesson about life and mortality. Most kids don't think about death and their own mortality; however, Leslie's death teaches Jess that life is a gift that can be taken from anybody at any time.
Lastly, I believe that Jess learns that he should keep pursuing his artistic passions. Jess is a talented artist, but almost nobody encourages him to develop his talent. Even Jess's father isn't encouraging.
When he was in first grade, he had told his dad that he wanted to be an artist when he grew up. He'd thought his dad would be pleased. He wasn't. "What are they teaching in that damn school?" he had asked. "Bunch of old ladies turning my only son into some kind of a..." He had stopped on the word, but Jess had gotten the message. It was one you didn't forget, even after four years.
The only person that does offer encouragement to Jess is Miss Edmunds. She praises his abilities and tells him to keep working at it. She even takes him to the National Gallery, and Jess learns that his talents can be appreciated by others. Through Miss Edmunds, Jess learns that he doesn't always have to hide his artistic talent.