Summarize:

The one-handed backhand is a beautiful shot but has become less popular in recent years. However, it is still used by many players such as Roger Federer as a powerful weapon in matches. Start from the ready position with your feet pointing towards the net and your knees bent. You should be holding the racket with both hands while facing the net. This is the first step of the one-handed backhand and is essential for perfecting your shot. Start from the ready position and take one step forward with your right foot, pivoting on your left foot. As you step forward turn your body and shoulders sideways so that they are now perpendicular to the net.  All your weight should now be on your back foot. This will help generate power and pace when you take the shot. By turning your body sideways you can move in a sideways and upward direction with your legs while taking your shot. Choose your grip based on the execution you want to achieve. The one-handed backhand will usually use an Eastern backhand grip to create topspin on the ball. Relax your dominant hand and use your non-hitting hand to rotate the racket to the appropriate grip. Grip the racket with your dominant hand once more. Ideally this should happen at the same time as you pivot and turn your shoulders.  To achieve the Eastern backhand grip use your left hand to hold your racket in front of you. Point the grip to the right and orient the string area perpendicular to the ground, facing you. Hold your right hand straight out directly above the grip. Bring it directly down so your base index knuckle rests completely on the top facet of the grip, and close your hand around it squarely. An alternative grip includes the Extreme Eastern or Semi-Western Backhand grip. This grip is for use by stronger, more advanced players and is good for hitting high balls but not good for hitting low balls. Another alternative grip is the Continental grip, which holds the racket at a 45 degree angle and is good for hitting slices. The Semi-Western backhand grip is a rare backhand grip that is good for hitting heavy topspin but bad for hitting flat shots and slices. The pivot and shoulder turn begins to take the racket back but you must continue to rotate your shoulders and move your arms until the tennis racket is all the way back and your shoulders are all the way sideways. Let your racket drop down as you straighten your hitting arm. At the same time step into the shot with your front foot. The drop of your racket creates the topspin on the tennis ball and is very important to your one-handed backhand.  This step is the transition from the preparation to the swing. Keep your non-hitting hand on the racket as you complete this step. Make sure your eyes stay on the ball so that you can anticipate the ball’s location and height. Let go of the racket with your non-hitting hand after your racket is down and your hitting arm is completely straight. Swing your arm and the racket to the contact point with the tennis ball. You should make contact in front of your body.  Make sure your arm and the racket swing from the shoulder as a unit. This way your arm position relative to the racket does not change as you swing. The racket should come as low as your knee right before you make contact with the tennis ball. This will produce the topspin that you want on your backhand. Your upper body will rotate slightly back towards the net as you make your swing. Your eyes should be totally focused on the ball as you make contact with the ball. Make sure contact is made in front of your body to enable you to maximize power and topspin. Keep the relationship between your arm and the tennis racket the same as you follow through. Continue lifting your arm and rotating your shoulders all the way through the shot, keeping your arm position the same. The relationship between your arm and racket should not change until your hand is at the same level as your head. Your non-hitting arm should extend all the way back and behind you. This arm controls how much your shoulders and upper body rotate as you follow through. Letting your non-hitting arm extend behind you limits the rotation of your upper body, helping you recover faster and stay balanced during your shot.
Work on your one-handed backhand if it feels more comfortable. Start from the ready position. Perfect your pivot and shoulder turn. Adjust to the proper grip. Complete your back-swing. Drop your racket and straighten your hitting arm as you step with your front foot. Swing the racket forward to contact. Make contact with the ball. Follow through your shot. Allow your non-hitting arm to straighten behind as you follow through.