Learn how and when to shift gears on your bicycle

If you have been riding a multi-gear bicycle for a while then you have hopefully figured out a shifting style that works. If you are new to pedaling this guide may be of some use.  

Many people use only a couple of gears while pedaling. Unless the area you are biking is limited to one landscape type (i.e. flat, level with no stops), not shifting will be inefficient - a waste of your energy. You might also think of it as not utilizing all available energy (i.e. momentum).
For example, if you are pedaling in a low gear while going downhill you are not adding anything to your speed, in which case you might want to stop pedaling and simply coast along. On the other hand, if you shift to a higher gear you can easily add speed without expending much additional energy. Conversely, if you are in a high gear going uphill you need to work much harder to successfully climb that hill. A lower gear will be slower, but noticeably easier. 

My personal style, while riding on roads in New England, is to try to use nearly the same amount of downward force regardless of the terrain, shifting fairly often to compensate. This works well probably 80% of the time. The remaining 20% will be steep hills, either up or down. As a result of this style I likely shift more often than most. Could be riding motorcycles for thirty years has contributed to near-obsessive shifting.    

I have tried to display the main aspects of pedaling in the graphic that follows. In addition to this visual aid there are plenty of very good resources with written descriptions covering gear ratios and shifting patterns (i.e. pedaling while shifting; not shifting both front and rear at the same time, etc.). See links at the bottom of this post.

The last thing I'd like to mention is that when mountain biking you will get the biggest gains by shifting to match the terrain. Actually, not shifting will not only make it more difficult but also more dangerous. You want to always be able to add some speed when needed. Being in the right gear will help in more ways than one. 

Have fun out there!

REFERENCES: 
1. Home of the yellow-blue-green graphic above.
2. Great written guide
3. A 2nd written guide with added graphics.
4. A very visual guide.