You're almost there. The problem is that while you have correctly declared the instance variables y , x , radius etc. in the line immediately below class Ball() {, you then declare a separate set of the variables with the same names in the Ball constructor. As far as Processing is concerned, this new set used by the constructor is completely independent of the instance variables that are used by display(), so their initialisation has no effect once the constructor has completed. The solution is to initialise these values in the constructor but not declare them, by removing the float , and int declarations:

Ball bounce1;
void setup()
{
  size(200, 200);
  fill(100, 204);
  bounce1 = new Ball();
  frameRate(30);
  colorMode (RGB);
}
void draw()
{
  background(0);
  bounce1.display();
}
class Ball {
  float y, x, radius, speedX, speedY, directionX, directionY;
  int ballColor;

  Ball() {
    y = 30.0;
    x = 30.0;
    radius = 20.0;
    speedX = 1.0;
    speedY = 1.0;
    directionX = 1;
    directionY = 1;
    ballColor = 150;
  }
  void display() {
    fill(204, 102, 0);
    ellipse(x, y, radius, radius);
    ellipseMode(CENTER);
    stroke(5);
  }
}

Because you declare the class variables again in the Ball constructor you're making those variables local to the constructor and not setting the values to the class properties that you reference in the display method.  To put it another way, remove all the type statements from the constructor - like this:

1.   Ball() {
2.      y = 30.0;
3.      x = 30.0;
4.      radius = 20.0;
5.      speedX = 1.0;
6.      speedY = 1.0;
7.      directionX = 1;
8.      directionY = 1;
9.      ballColor = 150;
10.   }

On a point of style, it's generally considered bad practice to lump all variables of the same type onto a single line as you do with the float variables in your class.  Putting them onto separate lines may take longer to write but it makes your class more 'readable'.