It's hard to believe today--especially since you can just look up at the sky and see our crater-covered moon with your naked eyes--but there was a time when people weren't intimately familiar with what the surface of our nearby neighbor looked like. Before the Renaissance-era invention of the telescope, the moon was generally thought to be a perfect, unblemished sphere. These days, with even a moderate telephoto lens, you can photograph the moon and see the surface details for yourself.
What you'll need
To shoot the moon, the technique is the same whether you have a compact digital camera or an SLR model--the only caveat is that no matter what kind of camera you choose, it should have a manual exposure mode, in which you dial in the aperture and shutter speed separately. So although many compact cameras will work just fine, if your camera is a true point-and-shoot with just a bunch of scene modes to choose from, you won't have much luck shooting the moon.
Something else to keep in mind: The bigger your zoom, the more dramatic your moon photos will be. After all, your subject is 250,000 miles away, so a wide-angle lens will have a hard time capturing the scene. If you're lucky enough to have more than 400mm, that's awesome. That might sound like a mighty big lens, but keep in mind that many common "megazoom" compact cameras can reach up to 1000mm--it's almost like having a telescope nailed to the front of your camera.
If your camera doesn't reach quite that far, don't worry; you can still get a great photo, and you can crop it afterward to put more emphasis on the moon.
Using a tripod is also a good idea. You'll be dialing in a shutter speed that's slow enough that you won't be able to keep the camera steady (especially when you're zoomed as far as the lens will go) without a little help.
If you don't have a tripod, find something--a nearby tree, a window, a wall, the hood of a car, anything--against which you can securely steady the camera.
Finally, you'll get better photos if you can trigger the exposure without touching the camera. To do that, you can take the shot using your camera's self-timer mode. That way, you can press the shutter release and the camera will take the shot several seconds later, vibration-free.
Dial in your camera settings
For the best results, switch your camera to the Manual exposure mode so that you can set the aperture and shutter speed yourself. Set an aperture of f/16 and choose a speed of about 1/100 second (or as close to that value as your camera allows).
Why those numbers in particular? Well, longtime photographers might recognize this setting as what used to be called the "Sunny 16 rule," a guide to getting a good exposure in daylight back before the invention of cameras with built-in automatic exposure meters. These are the exposure settings you'd use in midafternoon, for example. They work in this situation because the moon is simply reflecting sunlight, and it's the moon that you want to get a good exposure of--not the surrounding blackness of space.
Take the shot using the Sunny 16 settings, and review the shot in your camera's LCD screen. Then feel free to under- or overexpose the photo a bit to get the result you like.
Scene modes are a bust
What if you own a compact camera that lacks a manual exposure mode? You might expect that one of your camera's many exposure modes will do the trick, but unfortunately none of them are up to snuff. Regardless of camera or mode, automatic and semiautomatic exposure settings tend to misjudge the conditions grossly when you point your camera at the night sky and shoot the moon. To confirm, we experimented by shooting the moon with every available setting on the Nikon Coolpix L810. None of its roughly two dozen scene modes came close to exposing the moon properly. Not even using the exposure compensation control to underexpose the photo by two full stops could salvage the shot. The moral of the story? If you plan to ever do creative photography, including night shots such as this, be sure that your next camera has a manual exposure mode in addition to the usual bevy of automatic and scene modes.
Can smartphones play along?
Suppose you see the most awesome full moon of your life, and all you have with you is an iPhone. I have some bad news: You really have no practical way to get a good photo. In this case, a few forces are working against you. Not only does the lack of exposure control mean that the moon will be an overexposed blob of white, but your phone's relatively wide-angle lens means that the moon will be tiny. And the relatively slow shutter speed will blur the scene unless you can stabilize the camera by holding it extremely still, or by mounting it on a small smartphone tripod or leaning it against something immobile, like a wall. This is one of those situations where owning an advanced megazoom compact camera really comes in handy.