Processing will tell you when the mouse has been pressed by calling mousePressed.  You can do something in that function to record that a mouse pressed has occurred and decide what to draw based on that variable.

1. boolean hasMouseBeenPressed = false;
2. 
   
3. void setup() {
4. }
5. 
   
6. void draw() {
7.   if (hasMouseBeenPressed) {
8.     // do the normal program stuff
   
9.     rect(10, 10, 50, 50);
10.   } else {
11.     background(255);
12.   }
13. }
14. 
    
15. void mousePressed() {
16.   hasMouseBeenPressed = true;
17. }

thanks so much Jonny!