Cadence explained.

 
Understanding Gears
Multi-speed gears allow you to climb hills comfortably that might force you to stand up and "pump" or even get off and push if you were riding a one-speed. They also allow you to go faster downhill or with the wind at your back.
Try to visualize gear shifting in terms of where the chain is, rather than by looking at your shifters.
 
The sprockets that are closer to the middle of the bike (small front, large rear) give the lower gears(forclimbing). The outer sprockets (large front, small rear) give higher gears.(for descending)
 
Try to avoid the gears that make the chain cross over at an extreme angle. These "criss-cross" gears are bad for the chain and sprockets. Especially bad is to combine the inside (small) front sprocket with the outside (small) rear sprocket. This noisy, inefficient gear causes the chain to wear out prematurely.
 
Cadence

Every cyclist has an ideal "cadence" (pedaling speed), and an ideal amount of resistance from the pedals. When you are pedaling at your ideal cadence, you are putting out the greatest amount of power that you are able to sustain efficiently. You select your cadence by shifting gears. The gear needed to allow your "ideal" cadence will depend on the slope of the road, the wind conditions, and your own condition at any given time.
Good cycle computers will give you cadence display which is very helpful in training  yourself to spin the correct cadence.
High or Low?
"Higher" gears put more resistance on the pedals. If you select a gear that is too high for  the conditions, it will force you into a slower cadence.
 
Pedaling slower than your ideal cadence is wasteful of energy. You also run a higher risk of muscle strains and joint damage, particularly to the knees and hips.
 
"Lower" gears make the pedals easy to turn, so it becomes easier to spin to a fast cadence.
 
Pedaling faster than your ideal cadence can allow you to generate an extra burst of speed, but you will tire yourself out too soon if you try to maintain an excessively fast cadence.
"Pushing" vs. "Spinning"
"Pushing" a high gear at a slow cadence(50-65rpm) is like power lifting. It is good for building  up muscle mass and bulking up your legs, but it does little for your heart or lungs, and you can hurt yourself if you overdo it. This should be only done in interval training as  a strength building excercise.
 
"Spinning" a lower gear at a rapid cadence(90+rpm) is more like swimming. The rapid motion, with many repetitions makes the legs supple and flexible, it is highly aerobic, and the light pressure that goes with this style reduces wear and tear on the joints. With practice "spinning" becomes easier and more comfortable.
Here are  links to cycle computers with cadence display.
http://www.chaindrivencycles.com/index.php?page=shop.product_details&flypage=flypage-
sparkstore.tpl&product_id=71&category_id=47&option=com_virtuemart&Itemid=108
and this one with Heart rate
http://www.chaindrivencycles.com/index.php?page=shop.product_details&product_id=70&flypage=flypage-sparkstore.tpl&pop=0&option=com_virtuemart&Itemid=73
Yours in cycling
Stephen