How do Moon phases occur?
Moon phases are changes in the visible portion of the lunar surface illuminated by the Sun. The Moon is seen mainly through reflected sunlight rather than producing its own visible light. Ordinary phases are not caused by Earth's shadow falling on the Moon.
Sun-Earth-Moon geometry
At new moon the illuminated hemisphere faces mostly away from us; at full moon it faces toward us. Quarter phases show roughly half the apparent disk illuminated. The new-moon-to-new-moon cycle lasts about 29.5 days, longer than the Moon's orbit relative to distant stars because Earth also moves around the Sun during that interval.
Eclipses and observing times
Not every new moon produces a solar eclipse, nor every full moon a lunar eclipse, because the inclined lunar orbit usually prevents exact alignment. The Moon can also be visible during daylight. Crescent orientation depends on location and time. Phase diagrams require attention to illumination direction and observer viewpoint; northern and southern hemisphere views differ in orientation.