Since we only see the lit portion of the Moon that is facing Earth, we see a Moon phase.  There are eight phases that the moon goes through and they always occur in the same order.  The Sun's light seems to move from right to left across the surface of the Moon.  The phases of the Moon are: 1) New Moon, 2) Waxing Crescent, 3) First Quarter, 4) Waxing Gibbous, 5) Full Moon, 6) Waning Gibbous, 7) Last Quarter, 8) Waning Crescent, and back to the New Moon. 

During a New Moon we can see NO portion of the Moon's surface that is lit.  We see only the dark side of the Moon.  This typically marks the beginning of the Lunar Cycle which lasts 29 ¹/₂ days.  The Moon is between the Earth and the Sun in its orbit. 

During the Waxing Crescent phase, we see on the right side a small sliver of the lit Moon. 

During the First Quarter phase, we see the right half of the lit Moon.  The Moon and Earth are now "side by side" in their orbits around the Sun. 

During the Waxing Gibbous phase, we see almost the entire right side of the lit Moon.

During a Full Moon, we see the entire half of the Moon surface that is lit.  The Moon is positioned behind the Earth and Sun.

During the Waning Gibbous phase, we see almost the entire left side of the lit Moon.

During the last Quarter phase, we see the left half of the Moon lit.  The Moon and Earth are now "side by side" in their orbits around the Sun.

During the Waning Crescent phase, we see on the left side a small sliver of the lit Moon.