New Moon
When the moon is between the Earth and the sun, it is said to be new. If you look at the night sky, you may think that a new moon means no moon, but this is not the case. A new moon rises and sets at approximately the same time as the sun, so it appears during the day instead of at night. During this time, it's dark side faces towards the earth, making it very dim and easily overpowered by the bright sky.
Waxing Crescent
For a week after the new moon, a growing silver sliver appears in the sky; this is called the waxing crescent. This is a transition phase, which means that it encompasses the changing shape of the moon for several nights. The crescent rises later after sunrise each morning and is best seen in the early evening.
First Quarter
A little over a week after the new moon, the first quarter appears. Half of the visible moon is illuminated during this phase, which occurs a quarter of the way through the moon's orbit. Unlike the waxing crescent, this is a primary phase, which lasts for only one night. The quarter moon is at its peak at sunset and slowly descends until midnight.
Waxing Gibbous
After the first quarter, the moon will appear more than half illuminated, but is not yet full. This phase is called the waxing gibbous. The moon will wax for approximately a week, growing fatter each night until the full moon. During this time, it rises in the afternoon and evening and sets in the morning.