You don't want to bounce off your calves like you do when running. Many factors are dependent upon the stairs you've chosen, but a good, long flight is best. At the top, without rest, turn around and come down. Go slow on your descents for the first two weeks, then speed up as much as you want. Keep in mind that down is the high-impact direction, so how quickly you descend depends upon what type of event you are training for.
Many people have no reason to ever take the risk of speed descending, while others thrive on it.
After a few of these I spend the rest of the time just trying to keep moving. The perfect 20-minute set has you feeling like you could go faster at first, but finding it hard to continue by the end. Over the last 10 minutes, the crest of each flight should have your quads pumped and you should really be sucking wind. If you're hurting at the top, take a break but walk around - don't stand. Four times a week for six weeks should have you ready for Everest.