What makes you "faster" on the ground isn't so much actual physical speed. It's pattern recognition, knowing when and where to move, and eliminating extraneous movement.
Things you can do to improve these factors:
1) Drilling fundamental movements. On the ground, stuff like technical standups, shrimping, granby rolls, etc. Standing, stuff like back steps, shots, etc. The Jason Scully video that drop bear posted has some good examples. Focus on clean technique more than speed.
2) 2-person drills and sparring. I am very fond of semi-live "pattern recognition" drills where one partner is feeding a limited selection of triggers and the other partner has to respond with the correct technique.
3) Thinking ahead. I've taught a few classes recently focusing on the transition from closed guard to open guard. I made the point that if you desperately hold on to your closed guard until your opponent forces it open and then try to recompose to some form of open guard, your opponent will very likely be ahead of you in the battle for grips and posture. The analogy I used was losing your apartment because you can't pay the rent. If you wait until you're being evicted and the sheriff is throwing your stuff out on the sidewalk, then you're going to be in a world of hurt. It's better to find a cheaper apartment and get friends to help you move on your terms and your schedule. Same thing with transitioning to an open guard. Establish your grips and make the transition on your own terms while your opponent is still setting up his guard break. If you're always thinking a step ahead of your opponent, you will seem much faster than you are.
