Papa is away much of the time, because he has to work on the railroad to make extra money for the family. He works hard to care for his family, even if having to leave for work means he can't protect them. But his example is always an inspiration.
… and he's not afraid to back it up. Papa may be wise, and he may always mean what he says, but he also "[swings] a mean switch" (2.64). Still, he's probably a pretty good teacher. Unlike his brother, Uncle Hammer, he isn't impulsive and is quite slow to anger: he "always took time to think through any move he made" (7.27).
Most of the time, though, he prefers to teach his lessons with words. Like this one:
Cassie, there'll be a whole lot of things you ain't gonna wanna do but you'll have to do in this life just so you can survive. Now I don't like the idea of what Charlie Simms did to you no more than your Uncle Hammer, but I had to weigh the hurt of what happened to you to what could've happened if I went after him. If I'd've gone after Charlie Simms and given him a good thrashing like I felt like doing, the hurt to all of us would've been a whole lot more than the hurt you received, so I let it be. I don't like letting it be, but I can live with that decision. (8.43)
Here, Papa knows that things would be worse if he gave Mr. Simms a beat down for how he treated Cassie. But, he also opens the door for Cassie to use the system against itself in the way she lures Lillian Jean into a false friendship, and then gets her revenge (knowing that Lillian Jean will be unable to do anything against her—see the "Characters" entry on Lillian Jean for the lowdown).
And that might be a lesson he didn't intend to teach.
One of the most important lessons Papa teaches Cassie is about the weight of sacrifice. Papa's decision to burn down part of his own cotton crop to save T.J.'s life could put the family's land in jeopardy. Next to his family, Papa values the Logan land most of all:
Look out there, Cassie girl. All that belongs to you. You ain't never had to live on nobody's place but your own and long as I live and the family survives, you'll never have to. That's important. You may not understand that now, but one day you will. Then you'll see. (1.17)
Papa's deep connection to his land makes his sacrifice for T.J. that much more significant—and shows that he values his community even more than his land.