You have to remember that code inside draw() runs about 60 times a second, to update what it seen on the screen.
I suspect that you'll want to look into the keyPressed() function too...

So should I add other code outside draw()? How would I get back into the draw() after I have left it?

So what you need to do is map out the different gameplay phases.

All of this makes perfect sense except for one thing. If draw runs over and over again 60 times per second, how do I exit draw? And when I do leave draw, and enter a new "phase", how can I reenter draw?

Try running this:

1. void setup(){ size(200,200); }
2. void draw(){
3.   background(random(255),random(255),random(255));
4. }

This makes the screen flicker random colors, because draw() is being run over and over again (automatically) to redraw the screen, and each time it's redrawn, it uses a different random color for the background. There is no need to tell draw() to, or not to, run.

Now try this:

1. int state = 0;
2. void setup(){ size(200,200); }
3. void draw(){
4.   background(0,0,255);
5.   if(state==1){
6.     background(255,0,0);
7.   }
8.   if(state==2){
9.     background(0,255,0);
10.     fill(0); noStroke(); rect(map(millis()%1000,0,1000, 10, width-30),10, 20, 20);
11.   }
12.   if(state==3){
13.     background(random(255),random(255),random(255));
14.   }
15. }
16. void keyPressed(){ state++; state%=4; }

This time we see a simple program that can find itself in one of four states: Blue, Red, Green+Moving_Black_Rectangle, or Flickering. Moving between the states occurs when a key is pressed, which cycles through the states. In a sense, it is "waiting" for user input to move between the states.

Notice that draw() just runs over and over again. It is already exiting and re-entering itself!

Maybe you should think of if it behaving like this: pretend that draw() calls draw() at the end of itself. In this way you can see how it runs endlessly.:

void draw(){
background(0);
// blah blah blah..
draw(); // DON'T ACTUALLY PUT THIS IN!!!
}

Stop the draw from looping:

First Remark
When the last line of draw() is reached the image build up in draw() is thrown to the screen.

The program goes back to line 1 in draw() then. And starts all over again.


Second Remark
When you call a function such as "printSomething()", draw() is left a that line in draw(), the program runs through printSomething() and then returns automatically to draw() in the line after the call to printSomething().

1. void draw() {
2.   printSomething();
3.   println ("back in draw()");
4. }
5. 
   
6. void printSomething() {
7.   println("now printing something from printSomething()");
8. }

see also the command "return" which lets the function return a value but also can make the program quit a function before its end (the program then returns automatically to draw() in the line after the call to this function as well): 
http://processing.org/reference/return.html

Greetings, Chrisir