How do you determine which way the moon is revolving around earth?

You can do this with just a few pieces of information and some observation. Like the sun, the moon appears to rise in the east and set in the west. We know that for the sun and for the moon these are apparent motions and not true motions. The sun, for example, doesn't go around the earth once a day. Based on this, some people might conclude that the moon moves around the earth from east to west. However, observation will show you that while the moon rises in the east, it rises roughly 40 minutes later each night than the night before. Now if you think about it, if the moon were actually moving from east to west, it would rise earlier each night and not later. Observing the movement of the earth and moon from far to the north, the earth is rotating anticlockwise; this is why the sun appears to rise over the eastern horizon in the morning. If the moon were moving from east toward the west, it would advance prior to its rising, and would appear in the east earlier and earlier each night. Instead, the moon is moving toward the east in its anticlockwise orbit around earth. As a result, it has retreated from the eastern horizon a little more each night.