There is an equally famous book, by David Craig, called On Singing Onstage, which is indispensible. Tips from his book (and my personal experience as a director and participant in musicals):

(1) You have to think through the meaning of the song lyrics very carefully beforehand, so that you are able to link the emotion(s) to the words and the music -- most singers underperform (this does not mean ham acting, it means making every moment count). What is the arc of the song, when is the most dramatic moment, the peak; etc. You might want to think about what movements to make, and when -- absolutely minimal, but there are basic things like shifting your gaze from left to right from time to time, and so on. Always start by singing straight ahead.

(2) Make sure you know what is your best key to sing in, talk to the pianist beforehand if at all possible to be clear about your entrance.   If the accompaniest is any good (you should learn this if possible), then his or her job is to follow you -- you have to assert control over the tempo from the first bar of your entrance.

(3) If you make a mistake, don't stop unless it is catastrophic -- directors are very interested in how flustered people get.

Lastly, remember that the best actors are not always the best at auditions.   

yours,

Peter T.