The Moon is tidally locked to the Earth, which means that it takes almost the same amount of time for the Moon to complete one orbit around the Earth as it does to rotate once on its axis. As a result, the Moon always presents the same face towards the Earth, and we do not see the far side of the Moon from Earth.
However, due to a slight wobble in the Moon's orbit called libration and the elliptical shape of the Moon's orbit, we are able to see a small portion of the far side of the Moon over time. This phenomenon allows us to observe about 59% of the Moon's total surface from Earth, but we never see the entire far side.
So, to directly answer your question, we do not see both sides of the Moon from Earth. The far side of the Moon, also known as the "dark side" (although it receives sunlight just like the near side), remains largely hidden from our view. It wasn't until the advent of space exploration and the first human-made missions to the Moon that we obtained direct images and observations of the far side.