Theory:

Formation of the phases:
Moon_Phase_Diagram_for_Simple_English_Wikipedia.gif
Phases of the Moon
 
Full Moon day:
When the moon is at the other side of the earth, farthest from the sun, the bright part of the moon faces the earth. This is known as full moon day. During the full moon day, the whole disc of the moon is visible. The illuminated portion decreases every day after the full moon day.
 
Waning phase:
From the next day, the size of the brightest part of the moon reduces and appears to be thinner. The sunlit portion of the moon facing the earth gets smaller in size, resulting in half-moon (last quarter) or less than the full moon (waning gibbous moon). This decreasing phase of the moon is known as the Waning phase.
 
New Moon day:
When the moon comes on the side of the Earth nearest to the sun, the sun's light falls on the other side of the moon, which is not visible to the Earth. The side of the moon facing the Earth will be in complete darkness. Hence, the moon is not visible on the fifteenth day, called as the New Moon day. The illuminated portion of the moon increases every day after the new moon.
 
Crescent Moon:
The next day comes the crescent moon, where only a small portion of the moon appears in the sky when lit by the Sun's rays.
 
Waxing phase:
As the moon moves from its position, its size gets bigger, resulting in a half-moon (first quarter) or more than half- moon (waxing gibbous moon). This increasing phase of the moon is known as the Waxing phase. The moon grows again and turns to a full moon on the fifteenth day.
 
Waxing phase or waning phase?
On seeing the Moon, one can easily find its phase.
Waxing means 'growing'. If the right side of the Moon is getting brighter, then it is in the Waxing phase.
 
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Waxing Moon
  
Waning means 'shrinking'. If the right side of the Moon is getting darker and if the left side is getting brighter, then it is in the Waning phase.
 
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Waning Moon
Reference:
https://upload.wikimedia.org/wikipedia/commons/6/6a/Moon_Phase_Diagram_for_Simple_English_Wikipedia.GIF