Use your feet and legs as much as possible! This not only makes climbing easier and faster, but safer as well.
Take the extra time to get a good "lock" with your feet and legs. If the rope is slipping between your feet, you are forced to use your upper body more than necessary to keep from sliding back down the rope.
Get as much distance with each pull as possible. To do this, bring your feet as high as you can each pull and then stand up and reach as high as you can for your next pull. Less pulls = less work and faster rope climbs!
Grab the rope with both hands above your head. Pull down on the rope while jumping a bit and you will be lifted into the air. Wrap the rope around one leg, and use your feet to pinch the rope, thus anchoring yourself.
Reach up as high as possible with your arms (some say no higher than your nose), and grip the rope tightly. Release the rope from your feet. Using your abdominals, bring your knees up to your chest. Re-secure your feet on the rope.
Stand up with your legs, and re-reach as high as possible with your arms. Repeat the inch-worm process until the top of the rope has been reached.
Loosen the grip of your feet on the rope when coming down. Support your weight evenly between your feet and hands, slide your feet down and place hand-over-hand on the way down.