1. That violence is real, it exists everywhere, and it is scary. He learns this specifically after encountering the Grangerfords and the Shepherdsons and the huge battle they have in the woods. He and Tom used to plan heists and murder with their gangs, but when he sees it really happening, Huck is greatly disturbed. When he gets back out onto the river raft, states,
"I was powerful glad to get away from the feuds...there warn't no home like a raft, after all...you feel mighty free and easy and comfortable on a raft."
2. That lying to good people to get gain from them is not a good thing. He learns this after each and every town that he goes to with the duke and king; they scam people over and over again, and he sees all sorts of unsavory types of people along the way. He especially learns it when the duke and king mimick being the Wilks brothers and con the entire family into it. At this point, Huck is getting fed up with these two sordid characters. Before this occasion, he was willing to coast, to go with the flow, but as soon he finds out what they are planning with the Wilks family, it is soon after that he leaves those two behind.
3. Don't trust most people; but you can trust a true friend. The duke and the king scam Jim in the end, betraying all of the kindness and trust that Huck and Jim had given them. The people in the towns seem gullible and kind at first, but can turn on you in a second. He encounters angry mobs from what used to be docile crowds, death threats, and betrayals. But Jim is his friend through it all, and if they stick together, it is okay.
Those are just a few ideas; I hope they help you to get started!