Phases of the Moon

New Moon

When there is a new Moon, you won't be able to see any part of the Moon. It is completely covered, and the Sun is blocked by the Earth.

Waxing Crescent

A tiny slither of light manages to show on the Moon. This is where the Sun hits one side of the Moon, and it increases as the days go on.

First Quarter

Simply named due to the fact that the first quarter of the Moon is now visible when it gets to this stage. This is about 8 or 9 days into it's cycle.

Waxing Gibbous

By this point, most of the Moon's day side is visible. The Moon is very much brighter in the sky at night.

Full Moon

The Moon is now at it's brightest, and the full face of the Moon is on show. In all technicalities, because this is the full illumination of the day side of the Moon, this would be considered to be the real half moon. By this point, the Moon is now rising at sunset, and sinking at sunrise, and will appear this way for a couple of days.

Interesting fact: the Moon has a full orbit around the Earth in 27.3 days, but it takes slightly longer (29.5 days) for it to show it's eight different phases, called a lunar month.

Waning Gibbous

The Moon will now shift to the opposite movement, and waning gibbous starts to show less of the Moon face from the right side.

Last Quarter

Again, it's now looking half illuminated from our perspective. The Sun is now illuminating around the point of horizon, and we can't see this. A last quarter Moon is also known as the third quarter. It will rise at around midnight, and set during the day at around noon.

Waning Crescent

The Moon is now showing it's last sliver of light on the left side of it's face, and in a couple of days past this, it will be completely "invisible" - at least to the naked eye - and show the New Moon phase to start over again.

Libration of the Moon

So, we know that the Moon is tidally locked, which means that we see one side of it at all times. While this is true, during it's phases, it looks like it wobbles. While it does this (you can see it through a telescope if you watch it carefully), you can see the "shoulder" of the object lights up slightly.

Depending on the position of the Moon, and during it's orbital path, which is slightly elliptical, we get to see a little more of the Moon's eastern side. When it's rotation gets a little ahead of the Earth's, we see more of it's western side. This motion is called "libration in longitude".

The same happens due to the 5 degree tilt of the Moon's orbit, and it appears to nod at us. From this, we can sometimes see more of the northern hemisphere, and also the southern hemisphere of the Moon. This motion is called "libration in latitude".

Earthshine

A phenomenon called Earthshine is when the Moon is lit up by reflective light from the planet shining up on the Moon. This usually happens during one of the crescent phases, and the sunlight reflected is enough to dimly light the darkened surface of the Moon.

Here is a YouTube video from Free School on the Moon phases: