Answers (2)
The moon orbits the earth and the rotation of the earth causes the apparent rise and fall of the moon. The time of "moon rise" and "moon set" is higly variable over the year but does fit into a calcuable table of times which are available online, I believe there is an app you can get that tells you the times of moon rise and moon set.. The reason for the variable rise/set times are because of variations in a set of values: earth rotational speed, moons orbital speed and their rotational relationship.
The moon's motion through our sky is similar to that of the sun, but different: Like the sun, the moon rises in the east and sets in the west (with some exceptions for observers in earth's extreme northern and southern regions). Like the sun, the moon doesn't move across our sky quite as fast as the stars do.