This illustration is excellent because it shows where the moon is in relation to Earth and the sun, and it shows what we see from Earth to make the phase. Notice that half of the moon (and Earth) are always illuminated by the sun, but due to the moon's position around Earth, we see different areas of the moon, some not illuminated. Since we are in the new moon phase today, the dark half of the moon is facing the Earth. It is called a new moon because the lunar cycle is starting again, a new cycle of moon phases. By the way, when we call it the "dark side of the moon", it's really the same side we see all along, because the same side of the moon always faces the Earth.