• From any location on the Earth, the Moon appears to be a circular disk which, at any specific time, is illuminated to some degree by direct sunlight.
• The Sun always illuminates half the Moon, but, despite common folklore, the Moon does not have a permanent dark side.
• As the Moon orbits the Earth, we get to see more or less of the illuminated half. During each lunar orbit (a lunar month), we see the Moon's appearance change from not visibly illuminated through partially illuminated to fully illuminated, then back through partially illuminated to not illuminated again.
• Although this cycle is a continuous process, there are eight distinct, traditionally recognized stages, called phases. The phases designate both the degree to which the Moon is illuminated and the geometric appearance of the illuminated part.
• New Moon, First Quarter, Full Moon, and Last Quarter phases are considered to be primary phases and their dates and times are published in almanacs and on calendars. The two crescent and two gibbous phases are intermediate phases, each of which lasts for about a week between the primary phases, during which time the exact fraction of the Moon's disk that is illuminated gradually changes.
• The phases of the Moon are determined by the relative positions of the Moon and Sun in the sky. First and Last Quarters occur when the Sun and Moon are about 90 degrees apart in the sky. In fact, the two "half Moon" phases are called First Quarter and Last Quarter because they occur when the Moon is, respectively, one- and three-quarters of the way around the sky (i.e., along its orbit) from New Moon. Note that we don't say 2nd quarter or 4th quarter and instead use full and new, respectively.
• The relationship of the Moon's phase to its angular distance in the sky from the Sun allows us to establish very exact definitions of when the primary phases occur, independent of how they appear. Technically, the phases New Moon, First Quarter, Full Moon, and Last Quarter are defined to occur when the excess of the apparent ecliptic (celestial) longitude of the Moon over that of the Sun is 0, 90, 180, and 270 degrees, respectively. These definitions are used when the dates and times of the phases are computed for almanacs, calendars, etc.
• The percent of the Moon's surface illuminated is a more refined, quantitative description of the Moon's appearance than is the phase. Considering the Moon as a circular disk, the ratio of the area illuminated by direct sunlight to its total area is the fraction of the Moon's surface illuminated; multiplied by 100, it is the percent illuminated. At New Moon, the percent illuminated is 0; at First and Third Quarters, it is 50%; and at Full Moon, it is 100%. During the crescent phases the percent illuminated is between 0 and 50% and during gibbous phases it is between 50% and 100%.
• The moon’s orientation (tilt) with respect to your horizon shifts throughout the night because we live under a curved dome of sky. 
• Observers in the Northern and Southern Hemispheres see the moon apparently upside-down with respect to each other.
  • In the Northern Hemisphere, a waxing moon (from new moon to full moon) increases its phase from right to left. The opposite is seen in the Southern Hemisphere, where a waxing moon (from new moon to full moon) increases its phase from left to right.
  • From the Northern Hemisphere, we look generally southward to see the moon (or sun) crossing our sky. From the Southern Hemisphere, people look generally northward to see the moon (or sun) crossing the sky.
• This simulation of moon phases might help.
  
   

• When two or more heavenly bodies appear near each other in the sky, they are said to be in conjunction.
• When two heavenly bodies are on opposite sides of the sky (differ in their celestial longitudes by 180°), they are said to be in opposition.
• When an inner planet (Mercury or Venus) in conjunction with the Sun is closest to the Earth (inferior conjunction), it appears in its "new" phase. When farthest from the Earth, on the other side of the Sun (superior conjunction), it is in its "full" phase. In both cases, the planet is visible only around sunset or sunrise. Otherwise, it is lost  in the Sun's glare.
• When Earth is positioned on a line between the Sun and another planet with a greater orbit (opposition), the planet is in its full phase and shines brightly in Earth's night sky. When farthest from Earth on the other side of the Sun (conjunction), the other planet also appears full, but is visible only around sunset or sunrise.
• Even the Earth has phases, as viewed from outer space. Here is a photo of a gibbous Earth taken by Apollo astronauts on the Moon.

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