It's been a long time since the “10-speed" bike was the ne plus ultra of biking sophistication when it came to gears. These days, especially in mountain bikes, you can get anything up to 27 speeds.
What are all these gears in aid of? Quite simply, they allow you to pedal at the same cadence - regardless of whether you're going uphill, downhill, or cross country.
However, the main reason why mountain bikes have so many gears is to assist you in climbing up those mountains!
The main thing to remember when shifting is that you must always shift while pedaling, otherwise you'll strip the gears.
Front Derailleur The gears are divided into two parts. There are three chain rings in the front, which are controlled by the left hand gear shifter. That's why there are 3 numbers to choose from on that gear shifter - to choose which of three front rings your chain will rest on. The “derailleur" attached to the gear shifter moves the chain from one ring to another.
When the chain is on the smallest of these three chain rings (1), pedaling will be very easy. This is called the granny gear. The second chain ring is for level, off road riding (2), and the third, or largest chain ring, is good for riding on pavement.
So if you want to use just those three gears, you can certainly do so. But, using the right hand shifter, you can take advantage of the increments of gears available to you.
Rear Derailleur The back chain ring is a cog set featuring seven, eight or nine cogs, depending on how many “speeds" you have (21, 24 or 27). Each cog is of a different size, and again, the smaller size cogs will enable you to pedal very, very easily - but not go very fast, while the larger size cogs will allow you to go further with each downward stroke of the pedal.
The best thing to do is to practice, practice, practice. Take your bike to a parking lot or somewhere where you don't have to worry about people, and shift from one gear to another, getting used to each one and how easy or difficult it is to pedal while in that gear.
People new to biking might be rather wary of shifting gears. Shifting always was a bit problematic during the “old days" - when one only had a pair of center mounted levels to work with, but now gear shifters - the twist type - are so easy to use that there is no reason to be afraid of shifting. Again, as long as you're pedaling while you shift, you won't hurt the gears.
Alastair Hamilton is a consultant who writes on many consumer topics like bicycles for http://www.bikecyclingreviews.com . You can find more information and resources on mountain bike reviews at his website.