What would be some examples of what Huckleberry has learned through the course of The Adventures of Huckleberry Finn that would help him gain valuable insights?
Huck has many experiences that should and do help him grown and attain insights. He does not, however, always retain these lessons and these insights as he moves forward.
Early in the book, Huck pretends to be a girl so that he can find out what the town is saying about Jim and what they are saying about Huck's "death". In this episode, Huck is found out right away. The woman he speaks to helps him anyway. This moment offers Huck the opportunity to see that some people can be trusted and that lying is not always a necessary defense. Honesty can serve just as well.
Huck, nonetheless, continues to lie throughout the novel. He does, at one point, repent for his deception. When he hurts Jim's feelings and Jim articulates a disapproval of this behavior, Huck humbles himself and vows not to fool Jim again. He realizes that his actions have an effect on others.
This lesson is put to the test when Huck finds himself in the mess of the Wilks funeral with the King and the Duke. There, he decides to be honest rather than to continue to hurt innocent people.
However, in the final, extended episode of the novel, Huck once again chooses to lie and deceive. He plays a part in torturing both Jim and Mrs. Phelps in order to carry out Tom's elaborate plan to free Jim. The lesson of the benefits of honesty and the insight that his actions could bring emotional harm to others seems to have faded quickly from Huck's mind.
One of the most important lessons that he learned is to differentiate between "common sense" and "irrationality". Throughout the novel, most of the characters he encounters show some degree of irrationality or nonesense in their actions: the slave Jim and his superstitions, his Pap and his obsessions, the "king" and the "duke" and their crazy shows to collect money, Tom Sawyer and his unnecesarily detailed plans to free Jim. When we compare the actions of these characters and the result they obtain with Huck's ideas and outcomes, we can detect more sense in the way Huck solves things. His humble acceptance of Tom's ideas don't involve Huck's appreciation. All the time he is making remarks about how he would have done things differently.
Another important lesson that he learned was to detach society's conventions from individual experience. Society at that time was not expected to treat blacks as equals or to have deep affection for them. Throughout their journey, Huck and Jim learn about the value of friendship and loyalty, and how it can break down those social constructions.