Start out by making sure you have the right equipment, including a large-capacity memory card and a digital camera with a long-focus lens (starting at 500mm long). This will enable you to take as many pictures as needed and to zoom in on the action on the court.
Shoot photos from behind the court, aiming your camera lens through breaks in the fence. Or if possible, take pictures from the sidelines and focus on capturing shots of backhands and forehands.
Make sure to poise your camera so you can prepare for a picture before the action happens. Begin pushing down on the camera's shutter seconds before a serve, backhand or volley takes place so you get the shot in time.
Keep your eye on the rackets when photographing a tennis match, and try to anticipate the next swing so that you'll get the shot of the ball hitting the racket before it's airborne.
Level your focus on the server for at least part of the tennis match to get some guaranteed action shots. Since the ball is constantly in motion, it's a good idea to capture routine serves on both sides of the net to get images of all players.