If you are dealing with racquet sports, you really need to be able to sprint quickly in very short bursts of no more than 15 yards (often shorter) at a time with the ability to recover and change direction quickly.
With that said, going out and sprinting as hard as you can in a straight line for 40 yards (like the much ballyhoo'ed speed test for American football) isn't going to be very important for you.
What you need to focus on first step quickness (getting you going in correct direction as fast as possible) and hip explosion (makes sure you achieve maximum acceleration once you are moving in a particular direction). Improving your acceleration to your top speed is going to be more important than increasing your top speed.
For actual running drills to improve this I'd recommend:
Those are popular in American football but would just as applicable to racquet sports.
As for lifts, you want anything that encourages explosion from an athletic position - box jumps, squats, cleans, dead lifts. Make sure those are part of your lifting routines.