The best way to learn about eclipses of the moon is to go outside and look at one. Plus, it's a good excuse to stay up late at night! Mr. Eclipse is a website that will tell you when the next eclipse of the moon is where you live. (if you live in North America, there's one on Dec 21st 2010; it will start at 11:40 pm.)
Just go outside (put a jacket on!) about ten minutes before the eclipse and look up at the sky. A pair of binoculars is nice but you can see an eclipse of the moon just fine, even in a city, with just your eyes. It's perfectly safe to look at the moon during an eclipse, just like any other time. You don't need special glasses. The eclipse will last a little over an hour.
One cool thing about an eclipse of the moon is that you can see for yourself that the Earth is round like a ball. As the eclipse gets going, you can see that the shadow of the Earth on the moon is curved - that's because the Earth itself is curved.