The book actually devotes a whole chapter to it. There is a rival Mafia family (the Bocchichios) who had gained a reputation as using members as negotiators/hostages in war situations between the other families. They were used by the other families as go-betweens to help settle disputes One of the members of this family was going down, as i recall, on an unrelated murder rap - he was going to the chair anyway.

Vito had some favors to call in from this family so he arranged for the other guy to confess to the murder and take Michael off the hook.

I know I've forgotten all the names and gotten half the details wrong, but that's what happened.