The issue is, properly exposing the moon means you should use the setting that would work for a bright sunny day. If you let the camera figure it out, all that black space will cause all the moon detail to be blown out. If you have manual settings, try setting the ISO at 200, aperture at f11 or f16, and the shutter at 1/200. Should get you in the ballpark.
Edit: the moon is actually dark grey, so you might want to open it up a stop or two, maybe at f8, if you want it to look shiny. A full moon isn't the best time, because a sidelighted (partly crescent) moon will show more detail.