Go through Saint Denis greeting the NPCs, and or tossing back small fish while fishing. But if you want to do it naturally than just simply look out for random events. Snake bite guy, dead horse woman, etc. Even doing chores at camp can raise your honor (they're marked by little black dots around the camp).However if your honor is really low I'd suggest just greeting npcs in towns, or better yet Saint Denis.

Yeah just be a good guy, help people in the wilderness, say hi to people in Saint Denis and give money to the poor and to that woman at the north side

The honor bar doesn't really progress til the end of the game so I would not worry about it too much

I stumbled across Rains Fall after chapter 6 at Emerald station, once you speak to him your honor skyrockets! :)

There's a limit to how high your honor can go until after a certain story mission late in the game when Arthur starts trying to make amends. I think it caps out at around 80% before then. Is that what's happening to you?

Honestly don’t worry about it early stages in the game. My honor was quite low right up until the final couple of chapters and then ended the game with over 3 quarters

Thx i am worried i will get bad ending again