An accurate, consistent throw is required in order to maintain a three ball cascade.
Start by standing with your feet approximately a shoulders width apart, and one ball held in your palm. Be sure you are in an area which has good light so you are able to see what you're doing. It's also a good idea to keep some distance between yourself and any breakable objects.
The throw should be a smooth scooping motion with your forearm, but there shouldn't be much movement in your upper arm, as shown in the animation. Toss the ball to approximately eye level (or maybe slightly higher to begin) and catch it with the opposite hand.
It is important that you keep your eyes focused at the point where the ball peaks. Don't follow the ball through the arc or stare at your hands, as this is impossible to do once you start juggling three or more balls. This may seem difficult to do at first, but you don't need to see your hands in order to make the catch.
Practice alternating hands, until your throws are consistent, and you can do 10 throws and catches without dropping.