Name another sport which has the same physical requirements as tennis. The only one even close is racket ball. Tennis workouts must be designed to work on your specific needs, not the general needs of other sports.
Tennis requires quick lateral movement, rapid speed forward and back, rapid rotational power, and great flexibility. Here are a few ideas to help you improve your tennis workouts and gain maximum power and ability.
For serving and overhead slams you must have great downward power. One of the easiest exercises to perform is done with a medicine ball. Grip a medicine ball in both hands stretching upwards as high as possible. Go up on the tips of your toes. Now as fast as possible throw the ball down forcefully in front of your feet. Do this move furiously. This uses almost identical muscles as required for ultimate power in your serves and slams.
Swinging the racket with power requires great twisting or perpendicular power. You can accomplish this in two easy ways. The first is back to the medicine ball. Hold it in both hands extended in front of your waist. Twist to one side pulling the ball back as far as possible. Now unwind quickly throwing the ball with power into the wall.
You can perform almost the same motion using a cable pulley system in most gyms. The advantage of the pulley system is you can work on one arm at a time. Make sure to establish proper foot position for your swing, and then rotate your body in the fashion you use for striking the ball.
Building an explosive first step and leaping ability is one important part of great tennis workouts. We can steal a page from a football workout for this one. Get a box for jumping on and off of. Leap quickly up onto the box and then quickly leap down. Choose a box which challenges your leaping a little. On your landing do not land and stay stagnant. Land and take two quick steps, alternating between moving left, right, or backwards. This simulates what you do on the tennis court when you leap for a hit and then must move rapidly to recover.
Two more important exercises you should add to your routine are single leg squats and single leg calf raises. Single leg squats are performed by holding the weight and putting one leg up on a bench or block behind you. This makes sure the leg is not used. Bend to 90 degrees with the one leg and power back up. Use dumbbells for added weight when you can easily do your own body weight. Single leg calf raises are done in the same way only raising high on your toes to work the full motion of the lower leg.
Tennis workouts need to focus on the body parts and motions you will actually use on the court. If you train in general methods you can still improve but not to the degree of specializing your workout. Becoming a more powerful hitter, faster on the court, and a more explosive leaper is all a matter of training.