These days, rappelling is usually accomplished by descending a rope with a harness and rappel device (such as Black Diamond's ATC or Bluewater's Figure-8). The rope is fed through the rappel device which connects to the harness and the rappeller is able to control the rate at which rope passes through the device; consequently controlling how fast he or she descends.
The rappel device is usually found on the front of the harness, however, in a type of rappelling known as the "Australian Rappel", the rope is fed through the rappel device on the rappeller's back, so he or she descends face-down. This rappel is used mainly for military applications; it's much easier to fire a weapon from an Australian rappel.
Rappelling takes a while to get the hang of. The transition from standing vertically on the side of the cliff to hanging on the rope, feet on the wall, butt out, is at first a strange one. First time rappellers are often timid and slowly descend the rope, whereas experienced rappellers go down in great bounds off the wall, or just fly down, barely slowing themselves at all. (This is all assuming there's a wall to go off. In free rappelling, there is no wall, one descends the rope without any surface to push off. This is often the case in caving.)
Rappelling is usually a secondary activity associated with climbing. Few people go out for "a day of hardcore rappelling(!)" It gets boring really quickly, and isn't really a challenge once you know what you're doing. It's great, however, to slowly descend a rope after redpointing that killer 5.11c.