Just because the sun has gone down doesn't mean you have to put your camera away. Moonlight photos can be done quite easily with the right equipment. I am not talking about pictures of the moon showing details, but using the sunlight reflecting off the moon as a light source.
You will need a tripod and a camera capable of taking long exposures in the 20 - 30 second range. In the days of film, photographers would use a device called a "bulb" to make long exposures. It was a hollow rubber ball that resembled a grenade. A four foot piece of thin hollow tubing was attached to the bulb and at the other end was a fitting that screwed into the top of the shutter release button on the camera. Squishing the bulb would result in air being forced through the tube and pushing out a small rod of metal at the other end. Since this was end was screwed into the shutter button, the rod would trip the shutter. You would continue to compress the bulb for however long you wished to make the exposure. Releasing the bulb would result in the rod retracting and closing the shutter. That is what the bulb setting was used for on the shutter speed dial.
Most modern cameras also have a bulb mode although you no longer get to squish anything. To access it you need to put the camera in manual mode. Depending on the camera, the shutter will either remain open for as long as you hold down the shutter button, or will open with one press and close with another. Some newer cameras also allow you to set a shutter speed manually of up to 30 seconds so if yours can do that just ignore all the babbling above.
Here are some examples taken while camping at Lake Mary in Mammoth, CA.
The lights on the far shoreline are from cabins. The first exposure was 20 seconds at F/5.6 and the second was 30 seconds at F/5.6, all at ISO 100. The second one looks much better to me, almost like a path across the lake and more detail. Don't be afraid to turn your camera for a vertical photo. Even though I lost some reflection on the lake because the moon was rising it still looks nice.
To sum it all up, find a full moon rising or setting over your favorite body of water. Mount your camera on a tripod. Use a 30 second exposure at F/5.6. Watch for the reflection as it only lasts for a short amount of time. Oh, and have fun while you are taking the photos. I sent my camping neighbor's kids out on a Snipe hunt. Earlier in the day I had rigged up some fishing line so I could shake some bushes and make some noise. We explained to the kids all about the secretive Snipes and how to catch them. The parents relaxed around their campfire while I took photos and pulled some strings. That was a fun night.
Regards, Park Ranger