There are four phases of the moon. Like a lot of learning figuring out and remembering how to tell at a glance which phase the moon is in has taken some time. A full moon is more obvious; it is big and round and bright and even has a man in it. A new moon is pretty invisible as it reflects zero sunlight. The waxing and waning moon phases only reflect light on either the right or left side of the moon as the phase progresses from waxing to full to waning to new.
Waning implies going away. When the moon is waning it is getting smaller, having already been full. A waning moon means light is being taken away. Waxing on the other hand reminds me of waxing the car, or waxing the hair off your legs (gross, I know). Either way think of waxing as adding something. In reference to the moon phase, then, a waxing moon means you are adding more light.
When looking at a partially lit moon how can you instantly know if it is waning or waxing. If the dark side is to your left and the light side is to your right it is waxing. The light moves from right to left, like reading a book in Hebrew. When the left side of the moon is lit the moon is said to be waning.
For an instant picture of the waxing, waning, full and new moon go to http://www.timeanddate.com/moon/phases/
The question still to be answered is the new moon phase called ‘new moon?’
Hm, there is always something to learn. Use multiple sources
such as text, diagrams, and videos. Be in a relaxed frame of mind.