Born Again Pagan
Join Date: Aug 2009
Location: Southwestern Ontario
Bikes: Schwinn hybrid, Raleigh MTB
Assuming your bike has a triple-ring crankset (the left hand-gear changer should show 3 gears) put it in gear #2 and leave it there for the time being. Just use the right-hand gear changer for now. Practice going up and down the gears as you ride. Lower numbered gears are great for going up hills, riding into the wind, or just for cruising slowly and enjoying the scenery. Higher numbered gears are for keeping your speed up once you get there; in other words, start off in a low gear and once you feel like you're pedaling too fast, change to a higher gear.
One thing to keep in mind is that you want to maintain a steady cadence, which is the number of revolutions made by your pedal strokes. Try to be consistent by finding a comfortable pace, where you're happy with the frequency of your pedal strokes, and adjust your right-hand gears as necessary to maintain that pace.
After you become comfortable with running through all of the right-hand gears you can consider using the left-hand gears. Gear #1 is considered the "granny" gear and is usually used for climbing hills, especially when loaded down with bags of groceries, camping gear, school books, beer, etc. Gear #3 is usually used for when you're pedalling too fast in the highest gears on your right-hand shifter, like going down hills, or when you're feeling particularly strong and the wind is at your back. Keep in mind that when your using gear #1 on the left-hand shifter, make sure the right hand shifter is in the lower gears (#1-4). The opposite is true for gear #3 on the left-hand shifter: Use it for the right-hand shifters higher gears (#4-7 or 5-8 for an 8-speed cassette). This will lessen stress on the chain and help you to avoid "skipping" gears.
The majority of my riding is done in the middle ring (gear #2 on the right-hand shifter). My bike has 8 speeds on the other shifter and that gives me enough range for 95% of my everyday rides. In the future if you graduate to a racing-type of bike and join a riding club you may find yourself with a double-ring crankset and spend most of your time on the big ring, but by that time shifting problems will be a non-issue for you. Have fun and ride safe!