Viewing an eclipse is a breathtaking event indeed. Our ancestors looked upon them in wonder and amazement - viewing them as omens and even worshiping them. Having focused their lives around the sun and moon for crop production, important ceremonies, and tracking the passage of time; it was a dreadful time when the light in the sky disappeared.
It's just as special today as it was then, although we now know that it's simply the alignment of the Earth, moon and sun. This event can only happen with a new moon (as there is no light reflected from the moon's surface as this time).
As the moon passes in front of the sun, it casts a shadow (in fact, two types of shadows):
The umbra is the dark, inner shadow cast by the moon. It blocks out all light, leaving only the sun's corona visible. There is a relatively narrow area falling inside this shadow as the umbra, which is around 165 miles in diameter. This small area is due to the cone shape of this interior shadow.
The penumbra is the broader, partial shadow cast by the moon. Just as the umbra is cast in a cone shape (from wide to small), the penumbra's cone is cast in reverse (from small to large); covering an area of around 3,000 miles in diameter.
If you are lucky enough to be within the moon's umbra, you will witness a TOTAL eclipse; a rare thing indeed. As a total eclipse settles in, you are able to view the corona surrounding our star, while within the umbral shadow. This is an awesome sight, although it can only be viewed from a very narrow track on our Earth's surface.
PARTIAL eclipses occur as you view the sun from within the penumbral shadow. As this is a much larger shadow, it's able to be viewed by more people. Although you don't get the effect of the full eclipse, you still get to view an awesome sight.
In addition to these most famous types, there are two other types of eclipses to consider as well.
ANNULAR eclipses occur much as a total eclipse does (within the umbra), except that the relative size of the moon is smaller than that of the sun, producing a bright ring surrounding the moon. This is due to the fact that the moon is too far from the Earth for the umbral shadow to make contact with the surface.
The final type is the HYBRID eclipse, otherwise known as Annular-Total eclipses. They are very rare and occur as the eclipse transitions from annular, to total, and back to annular again.
On average, two to five eclipses happen per year, although many years may pass before an eclipse hits the same location on the planet's surface. Although the duration times might vary (due to many variables), they typically average around five minutes of total darkness.
Calculating an eclipse is relatively easy, there are databases provided by organizations such as NASA which give you dates, times and locations of past and future eclipses. And always remember, when viewing an eclipse you should take care of your eyes. You should either use a pinhole camera, a solar projector, or even your telescope (as long as you have the proper filters).
So always be careful, and enjoy.