The best way to become faster is to wrestle with fast people. I remember a few years ago, I began practicing with some guys who were very quick and very explosive. Traditionally, I hadn't been exposed to a lot of that type of wrestling - as such, for the first few days, I didn't do so hot. But as I continued to go live with them, I made leaps and bounds; wrestling with fast opponents just teaches you to react faster and become quick yourself.
Drilling is also good for working on your speed - the more you drill a technique, the faster you'll be able to execute it. Explosive weight training (Olympic lifts and the such) are good for training explosivity as well, which in turn will normally increase your speed. But, in my opinion, the BEST way to get faster yourself is to wrestle fast opponents.