LeeD says to shadow swing in front of a mirror, which is fine, except for the fact that most mirrors are in houses and playing with this can lead to a lot of things being broken and destroyed. How many mirrors have you broken Lee? I now practice outdoors.
One of the traditional methods is to swing a racket without string as fast as you possibly can.
Despite the advice given by many people, you won't learn to swing fast by doing a lot of repetitions. In fact, too many repetitions, especially with a weighted racket, will probably train you to swing slower. Speed training is about becoming more explosive, and fast-twitch muscles tire quickly.
The optimal way to train speed is by keeping the repetitions low and the quality high. This is the way sprinters train. Use maximal effort and give yourself plenty of rest between sets. Remember to warm up fully before trying maximal effort to minimize injuries.