I used to call this exercise Evil Ball Abs because I felt that was descriptive. A dear client protested that that was a mean name, so it has since been renamed Pretty Princesses. No matter what you call it, it remains challenging.
The Amazing Stickie is demonstrating using an exercise ball, but the ball is not required. It is mostly useful as a distraction from how hard your abs are working: clearly you must be having fun since you are playing with such a great big ball!
To begin, lie on your back. Enjoy this feeling; it is sadly temporary. Hold the exercise ball between your hands and feet, arms and legs extended toward the ceiling. Transfer the ball so that you are holding it with just your arms. Lower both arms and legs until they are close to the floor, but not touching. Raise arms and legs back to the ceiling, handing the ball to your feet. Lower both arms and legs again and then raise them to the starting position. One repetition includes lowering the ball on the head side of your body once and on the foot side once. One repetition is a perfectly fine beginning set, but as you grow stronger, move up to five or ten repetitions per set.
If you feel strain in your lower back, do not do this exercise. Try just lowering your arms with your knees bent and feet flat on the floor or just lowering your legs with your arms down by your sides. As your abdominals get stronger, you will find you can do the exercise without lower back pain.