...without going Looney!
The Moon is our closest celestial neighbor. It is 400 times closer to us than the Sun. Through a strange quirk of coincidence the size of the Moon in the sky is nearly the same as the Sun. During a solar eclipse the Moon can eclipse the Sun and reveal the Sun's corona. Since the Moon orbits the Earth in a ellipse sometimes the eclipse is not so perfect and we get a ring or Annular eclipse. Not long after an eclipse takes place the opposite happens where the Earth eclipse the Moon and leaves it in a reddish shadow. By the way the next total eclipse of the Sun over the US will be on August 21, 2017. It will cut the US in half and run coast to coast!
While some people have romantic thoughts that the Moon is large object in the sky it is actually quite small. As a matter of fact you need a 1000mm telephoto lens to get the Moon to fill the field of a 35mm camera. A 500mm lens will stay in your view finder for around 1 second. That is more than enough time to shoot a decent image of the lunar surface.
Exposing for the full Moon is nearly the same as daylight. In daylight exposure for you can use the "Sunny 16 rule." The basic rule says a sunny day your aperture is f/16 and whatever ISO you are using your shutter speed will be the reciprocal value of that ISO. Hence ISO x 1/x seconds =shutter speed (i.e. ISO 100 @ f/16 your shutter speed is 1/100).
The Moon has a similar rule. We'll call it, "the Looney 11 rule." The Looney 11 rule sets your f-stop at f/11. The Moon, like the stars is moving in the sky. To prevent blowing out the image and capturing the Moon the exposure depends on the phase of the Moon. A full Moon exposure is 1/400 of a second @ f/11 at ISO 400. A Gibbous Moon would be 1/200 @f/11 at ISO 400. A Quarter Moon is 1/100 @f/11 at ISO 400, and a crescent is 1/50 @ f/11 at ISO 400.
Now there are other ways of accomplishing the capture by changing the aperture or changing the ISO. If the Moon looks over exposed you can adjust accordingly. If it is slightly under exposed this is much more forgiving so long as it not too underexposed.
When the Moon is only two day old or just before it is a New Moon, there is a slim crescent and the shadow of the Moon can also be seen as the Earth also reflects light off the surface of the Moon called, "Earthshine." I like to expose to see the dark details of the Moon with the Earthshine to make it more interesting.
There are a lot of resources on the Internet that explain the "Sunny 16 rule" and the "Looney 11 rule" in depth. This should help you at least get started with an object that is out for much of the month as it changes in its waxing and waning phases.