Table tennis is a very delicate game. In order to excel, you must have excellent hand-eye coordination, paddle grip, and power control. The key to all of these is practice.
Everyone perceives their surroundings differently. In table tennis you must focus your eyes on the ball. This involves anticipating whether the ball will land inside or outside of the bounds. Determining this is not easy, but one tip is to focus on what angle the ball is returned at. If you can predict where the ball will land, then you will know where to position your paddle in order to return the ball.
In unison with your eyes, you must also move your hand (with the paddle) to bounce back the ball. This involves being able to move your hands without looking at them. The key to this is to keep your eyes focused on the ball and move your hand into your field of vision. By putting your hand into your vision, you are able to focus your attention on the ball and determine where your hand has to be in order to return it.
There are various paddle grips in table tennis, well there are actually a few with many variations. Shakehand is a good grip for beginners, this grip has the player place there index finger on the back of the paddle which allows easy control over the angle of the paddle.
Penhold is a special grip where you hold the handle like you would a pen. Wrapping your index finger and thumb around the handle while placing your other fingers on the back of the paddle. This gets rid of the need to switch between the sides of the paddle when returning the ball.
Power control can either be difficult or easy depending on the player. You must know your own strength in order to control it. If you apply too much force to your swing, then it will go out of bounds. If you apply too little force, then it won't go over the net.