What's the best way for someone to use their time with a chess coach? Let's say you have a 2 hour session. What questions would the serious player studying with a chess coach ask? Could you provide some examples?
The main advantage of a coach is the feedback.  Neither a book nor software can explain where your weaknesses are.  A coach should be able to review your games and explain where your weaknesses are and provide reference material to help your improve.
Once you know your weaknesses, you can use books and software to help yourself improve.  However, some chess concepts are too subtle to be explained to all but the most motivated.