If the light in on the left of the moon, it is waning. If it is on the right, it is waxing (moving towards a full moon). See related link below.
The lighted half of the moon is always facing the sun. The entire dark half of the moon is facing earth at the time of "New Moon".
At the time of First Quarter and Third Quarter ... when the moon looks like half of a disk in the sky ... you're looking at half of the moon's light side and half of its dark side. Of course, you can't see the half of the dark side that's right there in front of you, because it's dark.
in the new moon, the lighted half of the moon is facing the sun and tha dark side faces the earth.
At just about any phase, you can see half of the Moon's surface. Close to new moon, however, it may be hard to see the dark side.
The Waning Phase in the lunar cycle occurs as the moon shrinks from the Full Moon to the New (Dark) Moon. Note: You can tell when you are in the Waning Phase when the Left Side of the Moon is illuminated. Conversely, if the Right Side is illuminated, the Moon is Waxing.
On the opposite side from where the light is hitting the object. If the light side is on the left and the dark side is on the right, then the shadow is also on the right.
That phase is called the third quarter or it could be called a waning half moon.
half moon
waning
At just about any phase, you can see half of the Moon's surface. Close to new moon, however, it may be hard to see the dark side.
right side of the moon
At the moments of First Quarter and Third Quarter, the half-disk that you see is 50% of the "light side" ... half of the moon's illuminated surface. The entire moon is still there in the sky. The 'missing' half of the disk is comprised of half of the moon's dark side, which you can't see at that time. Because it's dark !