Moon Phases & Faces

Why do we see the Moon changing shape on the night sky? Why do we see only one side of the Moon, and what's up with that "dark side"?

Lunar Phases

This will be a little visualization exercise.
Imagine that you are above the North Pole looking down on the Earth and the Moon orbiting around it. The Sun, shining from your right, illuminates the half of the Moon that faces it, this is the day side of the Moon.
From the Earth, we see the Moon changing shape: as the Moon revolves around the Earth, we see varying amounts of its sunlit day side and dark night side. This causes the lunar phases.

  

   Phases 1-8    --    source:Wikipedia

The phases are:
1. New Moon
2. Waxing Crescent
3. First Quarter
4. Waxing Gibbous
5. Full Moon
6. Waning Gibbous
7. Last Quarter
8. Waning Crescent

Look at the first image above and the corresponding phases below it. You will get what's going on once you imagine, for each phase, that you stand on the surface of the Earth, looking at the Moon.
For the 1st phase, you stand on the Earth and look in the direction of the dotted line. You have the Moon's night side above you, while on the side facing away from the Earth it's daytime. This night side is not visible to you, because it is not illuminated by the Sun, and the Moon doesn't have its own light source. So it seems to be a moonless night. This is called the New Moon. Similarly for the 2nd phase, as the Moon has moved a little on its journey around the Earth, you see some of its day side already: the Waxing Crescent. For the 3rd phase you already see half of the Moon's day side, this is the First Quarter, and so on.

Lunar Faces 

Let's choose a point on the surface of the Moon: make it the orange dot below.

 

First, focus on the Moon and the dot only. You can observe that the dot seems to move around the Moon's perimeter, but actually the Moon rotates around its own axis with the dot on it. So we know that the Moon revolves around the Earth once in one month, while it spins around its own axis once, in about the same time. Keep looking at that dot. It seems to move around the perimeter of the Moon once, while the Moon goes around the Earth once.

Now let's have another point on the lunar surface: the blue dot!



While the orange dot faces the Earth, the blue dot is on the opposite side. The dots will always stay on their respective sides. So the orange dot is visible from the Earth when lit by the Sun (when it's on the white side), but you can never see the blue dot from Earth. The hemisphere of the orange dot is called the Nearside of the Moon - we always see this same lunar face from Earth, while the hemisphere of the blue dot is the Farside, sometimes called the "dark side"...
One more look at that blue dot. It is sometimes on the sunlit (white) side, sometimes on the night (dark) side, the same way the orange dot is, as the Moon spins around its axis. So there is no permanent "dark side", only day side and night side in one lunar day, and visible Nearside and never seen Farside.

Neaside and Farside   --   source: Britannica.com