Tennis Grips
 
 
Name of grip
Image of grip
1. Eastern forehand grip 
Note that the eastern grip is popular with beginners and is widely used with forehands because of its comfort.  The grip can also be used to hit backhands, serves and volleys.  Here is how to make the grip: 
  1. Hold the racket in front of you in your left hand (or right hand if you’re a left-handed player). 
  2. Rotate the racket so that the face (strings) of the racket is perpendicular to the ground. 
  3. Lay the palm of your free hand flat on the face of the racket.
  4. Move your palm toward your body, down the shaft of the racket, until it hits the end of the handle. 
  5. Wrap your fingers around the handle and space them slightly apart. Your thumb and forefinger should lie almost directly on top of the handle, forming a V that points toward your right shoulder (toward your left shoulder if you're left-handed). Your thumb should lie across the top of the handle. 
Tips: An eastern grip is also called a "handshake grip" - it's like shaking hands with your racket
    Eastern forehand grip
2. Western forehand grips 
Note that the western grip is excellent in forehand play but feels awkward for beginners, especially when used for backhands, serves and volleys. Advanced players often use it to enhance their forehand play.  Western Grip Steps:  
  1. Start by holding the racket with an eastern grip. 
  2. Relax your grip and turn the racket counterclockwise until the top of the racket points toward the "11 o'clock" position. Left-handed players should turn the racket clockwise to the "1 o'clock" position.   This is grip is sometimes referred to as a semi-western grip, see diagram (a) to the right.
  3. For a full western grip follow the same procedure as in '2' above except rotate the top of the racket until it points to "10 o'clock" position ("2 o'clock" for left-handed players).  See diagram (b) to the right.

  4. Wrap your fingers around the handle and space them apart slightly. The V formation should point to your right (or left), and your thumb should lie across the top of the handle. 
(a) Semi-western grip 
(b) Full-western grip
3.  Single-handed backhand grip, also the continental forehand grip 
Note that the continental grip is used by more advanced players in serving and volleying.  Grip steps: 
  1. Begin by forming an eastern grip. 
  2. Ease your grip and turn the racket with your left hand (or right hand if you're a left-handed player). 
  3. Turn the racket until it is perpendicular to the ground, or pointing to the "12 o'clock" position. Then, if you are right-handed, turn the racket to about the "1 o'clock" position. If you are left-handed, turn the racket to the "11 o'clock" position. 
  4. Wrap your fingers around the handle and space them slightly apart. The V formed by the thumb and forefinger should point toward you, and the thumb should lie along the length of the handle. The bottom knuckle of your index finger should lie right on top of the racket. 
The continental grip is often used for a single handed backhand grip.  The more the racket is turned away from the body (" 1 o'clock" position above) the more the thumb is placed at the back of the racket as a back-bone to the backhand shot.  This grip is often referred to as the Eastern backhand grip.
    Continental grip 
        Backhand grip
4. Double handed grips 

Note there are many variations on the double-handed grip based on the forehand grips with the other handed added.  

The most common backhand grip is the single-handed backhand grip (eastern backhand) with the other hand added on top and touching the lower hand.  For right-handed players the left hand (top hand) grips the racket with a Western forhand grip for a left-handed player. 

Link to Tennisone.com for more insights on the double-naded backhand. 
 

(a) Right hand double-handed grip 
(b) Left-hand double-handed grip
Grip variations and overall tips 

Between an Eastern and Continental grips is the Chopper grip.  This grip can be used as a beginner grip and reduces the need to change grips in order to hit forehands and backhands. 

The reverse angle view of the grip shows how the fingers should be spread around the rackethandle and relaxed.  The thumb should be supporting the racket pushed against the side of the racket handle.  It is important that the grip is relaxed until shot execution to reduce the liklihood of developing tennis elbow.  To assess grip size click here. 

Overall Tips: Choke up, or slide your hand toward the racket's face, for more control. The amount of control depends on which stroke is used.  Don't squeeze the handle too much, and keep your arm relaxed while swinging. Keep your wrist straight and your fist tight so that the racket doesn't spin out of your hands. 

The best grip is the one that's most comfortable for you.  If you find grip variations that work particularly well, use them.

    Chopper grip 
 Reverse of Eastern grip
Important link for understanding how to use tennis grips when playing 
Building Blocks of Tennis: Grips are the Cornerston
Some material drawn from ehow.com