Summarize:

Your leading foot (right if you're right-handed) should be slightly farther away from the table than your other foot. This will allow you to angle your body away from the table. You'll use this position to get more power when you turn your body into the serve. Your stance should be strong and steady. Not only will this keep you balanced as you get ready to serve, it'll also let you move quickly when you need to return the ball. Lean over from your waist, rather than your chest. Keep your shoulders back and open. Check your balance to make sure your lean makes you feel steadier. This position is perfect for getting your arm in position to use your wrist and forearm when you serve. Keep your arm loose and don't lock your elbow. Move your racket back and slightly up after you throw the ball. Then bring your arm forward, turning your body and shoulder as you do so. This is a backspin serve, so hit the ball from the bottom with an open racket. Stay focused on the ball throughout the throw and serve. Move your racket back and slightly up after you throw the ball. Bring your arm forward by turning your body and shoulder. Right before you make contact with the ball, put your racket into a closed position and strike the top of the ball. Stay focused on the ball throughout the throw and serve. Backhand serves involve a different arm position. Position the racket in front of your body by turning your arm across your torso. These serves can also involve different kinds of spin. Serves with sidespin are usually delivered from the backhand position. Stay focused on the ball throughout the throw and serve.
Angle your body about 45 away from the table. Bend your knees and keep your legs shoulder-width apart. Bend your body forward slightly for balance. Hold your racket ready with your elbow bent at a 90 angle. Move the bat down and forward for a forehand backspin serve. Hit the ball up and forward for a forehand topspin serve. Turn your arm across your body for backhand serves.