If you lived on the Moon, would you see the sun rise and set? how about the earth?
Just watch the Moon each night from your backyard, noticing the movement of the terminator (the moving boundary between light and dark, not Arnold) as its phase changes from crescent to first quarter to gibbous to full. Anyone standing on the surface of the moon would see the sun gradually rise as the terminator passes them and the area goes from dark to light. As phases continue past full, and you see the moon go from full to waning gibbous to third quarter and waning crescent, anyone on the Moon's surface at the terminator would see the sun setting. As the Moon orbits Earth, it always keeps the same side facing us. This, combined with the fact that it takes 29 1/2 days to complete one cycle of phases, means that anyone on the Moon's surface would see 29 1/2 days go by between consecutive sunrises or sunsets.
Now imagine yourself on the Moon's surface exactly in the center of its disk as seen from Earth. Since the same side of the Moon always faces us, you would see the Earth directly overhead at all times. There would be no Earth rise or Earth set. If you were at another point on the hemisphere of the Moon facing Earth, the Earth would be somewhere other than overhead but would still not move across the sky. If you were on the side opposite Earth you would never see it, just as we never see the far side of the Moon from Earth. One interesting exception to the above description would be for anyone exactly on the limb (edge of the Moon's disk as seen from Earth). The Moon "wobbles" or "nutate" over time in its orbit, so we can actually see slightly more than 50% of its surface over time. That mean someone at the limb could see the Earth just at the horizon, occasionally rising and setting briefly.
Paul Walorski, B.A., Part-time Physics/Astronomy Instructor
'The important thing is not to stop questioning. Curiosity has its own reason for existing. Never lose a holy curiosity.'