In the case of Sam and Max, prospective actors were given descriptions of the characters written by Steve Purcell, as well as samples of the voices from the previous Sam & Max game. We listened to one set of auditions in which actors tried to mimic the sound fairly closely, and another where we encouraged them to try something to give it a fresh spin. For some of the actors, we asked them to audition again, with some more specific direction to help them hone in on the character's style.
In the case of newly created characters, we typically write up a brief summary of the character's personality, as well as some possible similar voices. For some, we have a fairly specific idea of the voice in mind. For example, Mr. Featherly the chicken actor was supposed to be reminiscent of Don Knotts on-camera, and someone like Patrick Stewart off.