The problem is that the moon is very bright but the whole rest of the picture is dark. The camera reads the -average- brightness of the scene and tries to split the difference, so the moon gets really badly overexposed.
First you need to control the exposure manually if possible. I can't tell you what combination of shutter speed, film speed, and f-stop to use, you'll have to experiment. But that's the beauty of digital cameras, you can take as many pics as you want, they cost nothing.
Secondly, if you're taking pics of the moon you're probably zoomed all the way out. This means any little tiny movement of the camera will blur the picture. So this is a situation where a tripod would be very useful.
If you take pics of the moon in daylight you'll get better pics because the whole scene is bright!