Full Moon
A full moon appears when the Earth is behind the Earth. Observers on the Earth are then presented with a view of the illuminated face of the moon. This places the Sun and moon at opposite points in reference to the Earth. At a full moon, an observer may witness the dawn Sun rising above the eastern horizon, with a full moon descending below the opposite horizon.
New Moon
When the moon is between the Sun and Earth, observers are presented with a view of the unlit face of the moon called a new moon. Because the moon lies near the sun in the sky, a new moon will rise at dawn with the sun. However, the new moon is often invisible at sunrise, washed out by the intensity of the sun.
Waxing Moons
As the moon waxes from new to full, the illuminated face of the moon increasingly supplants the darkened side until the entire face of the moon is illuminated. In reality, the half of the moon facing the Sun is continually lit---with the brief exception of lunar eclipses---but as the moon moves in its orbit around the Earth, observers are presented with a changing view of the sunlit and unlit sides of the moon. Waxing moons, including the first quarter moon, are hidden beneath the horizon at sunrise.
Waning Moons
After a full moon, the moon wanes as the moon appears to progressively darkens until becoming a new moon. Waning moons are visible at dawn. The third quarter moon, when the moon is halfway between full and new and appears half light and half dark, appearing at its highest point in the sky. A waning gibbous moon---describing a waning moon that is still mostly lit---appears in the western sky at dawn. A waning crescent moon---describing a waning moon that is mostly dark---appears in the eastern sky at dawn.