I wanted to test my new camera (Panasonic FZ200) so decided to take a photo of the moon. Out of the box, like 99% other cameras, the photo was bad. I changed Metering Mode to SPOT and took the photo again. Metering mode is in Set Up for any camera and usually gives three options: Smart/Evaluative/Matrix, Partial/Center-weighted, Spot. When you select Spot, camera looks at the light in the center only. Bring the Moon in the center of your screen and camera will do the job correctly. Try with your camera and let me know.
Most cameras use by default Smart/Intelligent/Evaluative/Matrix based logic for metering. That works well in most situation where light is more or less uniform. However if you have some very dark and some very bright spots in your photo, try switching to Center Weighted or Sport metering and you will see what you would like to see in your photograph. Also metering off of faces can get you better skin colors in portraits and in photos of people. Normally, I rarely use Maxtrix/Evaluative/Smart metering mode on my cameras.
Now here is a photo with Metering mode set to Spot: