How did Akela become familiar with the ways of men in The Jungle Book?

Akela doesn’t become familiar with the ways of men. Akela is the wolf that take Mowgli in and raises him as a part of the wolf pack. However, Akela knows the ways of the pack and teaches Mowgli the pack’s laws and customs. It is not until Mowgli meets Bagheera that he learns about how Bagheera knows the ways of men:

Yes, I too was born among men. I had never seen the jungle. They fed me behind bars from an iron pan till one night I felt that I was Bagheera—the Panther— and no man’s plaything, and I broke the silly lock with one blow of my paw and came away. And because I had learned the ways of men, I became more terrible in the jungle than Shere Khan (chapter 1).

Bagheera was born at the king's palace, and there he wore a collar and learned the ways of men. That is what makes Bagheera stronger than Shere Khan: he knows of men, and therefore, he is not afraid of them in the same way that Shere Khan is afraid of them. It is Bagheera’s knowledge of men that makes him the perfect character to take Mowgli back when he needs to return to the world of men.