* The moon's phases: The moon goes through phases, from a new moon (invisible) to a full moon (bright and fully illuminated). During the new moon phase, you won't see the moon even on a cloudless night.
* Moonlight and cloud cover: While clouds can obscure the moon, the moon's light can still be visible even on a cloudy night. The light will be diffused and less bright, but you might still be able to see it.
In short: On a cloudless night, the moon will be visible if it's not a new moon. Even on a cloudy night, you might still see the moon's light.