Photographing the moon always seems somewhat exotic to me because not only are you making a night (or at least a twilight) photograph, but you're also photographing a landscape that only a dozen or so people have actually walked on. Taking pictures of the moon is also fun because you get another chance--weather permitting--almost every night. Although I prefer to shoot the moon when it's full, it's also great to capture one of those thin silver crescents in the twilight sky.
Photographing the moon is very simple and you can even do it in your "automatic" exposure mode. Interestingly enough, the correct exposure for a bright full moon (excluding whatever landscape you have in the foreground) is the same as for a sunny day: about 1/250 at f/16 at ISO 200. And why not, after all, it's being illuminated by the sun! You may have to adjust your exposure a bit if you want some foreground detail, but as a starting point, I would just put the camera in auto (or try night mode) and check your first shots on the LCD. If it looks too dark, add some exposure using the exposure compensation dial.
There is one trick to shooting the moon though and that's being sure to include a good ground reference. When you look at a huge full moon (especially when it's first rising in the twilight sky) it looks huge and the reason is because you have the horizon or some other ground reference. As the moon rises in the sky it becomes smaller and smaller. That's why it's also good to consult a tide/moon chart and see when there is going to be a good full moon and get to your location before it starts to rise. That way you can get a number of exposures before the moon gets too high in the sky and the size diminishes.
Sometimes a great moon will surprise you, too. I shot the full moon and power lines here in Port Aransas, Texas after photographing a sunset (and the afterglow) intently for about an hour. I turned around to pack up my gear and saw this huge full moon, so I slapped my 300mm lens back on the Nikon D70s body and started shooting. Remember, the sun sets in the west and the moon rises in the east, so next time you're photographing a sunset, turn around and look for the rising moon! And check out my site for more tutorials on night photography.