The day of auditions is the first time you will meet your actors, even though at that time nothing can or will be cast. Of course, you will also meet a lot of other actors who, for whatever reason, don't seem to fit into what you envisage the show to be. So you watch people say their monologues, look at how they've internalized the character, how they say the lines. Is this someone who recites, or who makes you believe in what they are saying? Does this person make eye contact or are they not confident enough to do so? Are they willing to take control of the audition stage or are they stuck like deer in the headlights?
On the day of callbacks, your vision gets more concrete. Suddenly you are seeing this person against that person. Assuming they pick up on the character implied in their lines, does the height difference work, does the vivacity of person A work well against the stolidity of person B, do they interact together well and are inventive? Your mind starts seeing possibilities: he would be good for this character because he plays well against her, who would do equally as well as his wife. You try guiding the actors to see how they take to suggestions and instruction.
Finally, you have to make your choice. Her, him, him, her, etc. This cast will make the play work, make it zing. They're the chosen ones.
But of course, at rehearsal, you ultimately discover how they do work together, how they look together, how they act off each other.
And it's a miraculous thing.
Your cast will make you look at your vision again. Their interactions will make you realize that your concept was too limited: your actors make the play come alive -- these characters are no longer lines on a pages, they're human -- and they give you more possibilities for bringing out the possibilities and the nuances of the play.
You, as director, then merely channel their own visions and desires about their characters into the overall structure of the play. You no longer have to be all-knowing: the plot just comes alive.
Ladies and gentlemen, I have that cast for An Ideal Husband.