New moon: we see darkness (aka nothing)
Waxing crescent moon: we see a sliver of light that indicates the crescent (during this time, the moon moves eastward away from the sun)
First quarter moon: when half the moon's face is illuminated.
Gibbous moon: when more than half the moon is illuminated, we call this a gibbous
Full moon: we see the whole round moon, lit up.
Waning gibbous moon: when the moon becomes thinner, but is still lit up for over half of its shape.
Third quarter moon: this is where the moon shows the other half of itself (that we didn't see in the 1st quarter) while the other half is dark.
Waning crescent moon: when the moon is a thin crescent, traveling down into the darkness of the full moon.
This process takes about a month (29.53 days).