Recover as quickly as possible after every tennis shot, so you can come out of a split step just as your opponent is hitting his next shot.
We have a natural tendency to sprint after the next ball, but it takes discipline to recover after every shot so that we are balanced and ready to get to that next shot.
If you never sprint, you will never be as fast as you could be. Many practice sprinting with high intensity interval training (HIIT).
http://www.intervaltraining.net/hiit.html
If you have difficulty starting fast, stopping fast, quickly changing directions, and recovery, try these on court agility drills:
http://assets.usta.com/assets/1/USTA_Import/USTA/dps/doc_437_269.pdf
(Probably my favorites are the spider drill and horizontal repeaters.)
Want to make them even more realistic for tennis? Swing at the end just before you change direction, to better practice recovering in the opposite direction after a swing.
Want to help prevent the all-too-common shoulder, elbow and wrist problems as you bash that ball over and over?
Do the thrower's ten exercises:
http://www.muhlenberg.edu/pdf/main/athletics/athletic_training/throwers10.pdf
Have time off this winter? Get ready for the spring season:
Off Season Training
http://www.sport-fitness-advisor.com/off-season-training.html
You can even add in some weight training: Complete, Annual Tennis Weight Training Program
http://www.sport-fitness-advisor.com/tennis-weight-training.html