The grip in tennis is very important to insure the accuracy and speed of a serve.
At the right is the proper grip for the slice serve (go to
slice link). As shown, the hand is at a closed degree to the court, therefore the face of the racket is closed. The hand is wraped around firmly and the wrist is very solid. This is important because during a fast serve, like the slice, if your wrist is loose, the weight of the racket moving quickly could substancially damage your wrist (a sprain or pull). Some pro tennis players have been known to work out their wrists, just to gain strength there.

Hold your racket like you would a spoon.
Grab it with your palm facing downwards and slightly outwards. In this position you can become more flexible and have more control (and therefore accuracy in your serve).

Wrap your index finger around the racket to stable it. (Much like you would when cutting with a knife). This gives your hand support.

Before serving always remember to relax your hand, let the racket bounce around a bit and then take the right grip. This will help you get ready to serve.
The Grip
You need Java to see this applet.
Basic Serve
Sampras
Tips
Bibliography
Slice
Topspin
The Follow Through
Time Log
Grip