So, what’s been happening? As you know, the moon orbits around the earth (i.e. it has “proper” motion), corresponding to a movement relative to the background stars by an amount roughly equal to its own diameter each hour; this movement is from west to east i.e. the moon starts (as a new moon) low in the western sky and moves slowly “upwards” and eastwards. At the same time, due to the fact that the earth is turning on it’s own axis from west to east, the stars and the moon (and of course the sun) appear to move from east to west. It’s a bit like someone “walking up the down escalator” assuming the person is walking upwards slower than the escalator is going down, he or she will eventually arrive at the bottom of the escalator.
If you would like to know more about the motion of the moon, take a look here: http://en.wikipedia.org/wiki/Orbit_of_the_Moon
If you have a pair of binoculars you can take a look at some of the moons “seas”, you should be able to see (1) Sea of Crisis, (2) Sea of Fertility, (3) Sea of Nectar, (4) Sea of Tranquillity, (5) Sea of Serenity and (6) Sea of Cold.
Photo credit: The Universe Today