public void act()
{
     checkFire();
    //leave the rest of your player's act method alone
}
//after the "act()" method, add a new method:
public void checkFire()
{
   if(Greenfoot.isKeyDown("space")) {
       getWorld().addObject(new Bullet(), getX(), getY());
   }
}

public Bullet extends Actor
{
   public void act()
   {
       setLocation(getX() + speed, getY());
       checkBoundaries();
       destroyEnemies();
   }
   //we add a method "checkBoundaries()" that destroys bullets that are off screen.
   public void checkBoundaries()
   {
       if(getX() > getWorld().getWidth() - 1) 
            getWorld().removeObject(this);
       else if(getX() < 1) 
            getWorld().removeObject(this);
       if(getY() > getWorld().getHeight() - 1) 
            getWorld().removeObject(this);
       else if(getY() < 1) 
            getWorld().removeObject(this);
   }
   //"destroyEnemies()" destroys enemies.
   public void destroyEnemies()
   {
       //"Enemy" can be any class that you want the bullet to destroy. 
       Actor enemy = getOneIntersectingObject(Enemy.class);
       if(enemy != null) {
            getWorld().removeObject(enemy);
            getWorld().removeObject(this);
       }
   }

   private int speed = 10;
}