You can learn a lot about the Moon's movement by watching it--and you don't have to come out at night! Since the Moon spends half of its time in our daytime sky, the chances are good that you'll be able to see it at some point today!
Find out when the Moon is rising today—I use a weather app, or you can check a site like the one here. Use this information to see when you can view the Moon and the sun at the same time.
Once you've found the Moon, point one hand towards the Moon, and the other at the Sun and take note of the angle you make with your arms: this is the geometry of the Earth-Moon-Sun triangle.
Since you're on Earth and pointing at each of the others, you can see where the Moon is in its orbit. The only time you won't be able to see the Moon is when it is too close to the sun; this happens a few days before and after the New Moon phase. (Our last New Moon occurred on July 23rd, so if you look in the next few days, you should have no problem finding it).
This video shows you how to measure the Moon’s location with your arms. It was posted when the Moon was a crescent on about day 24 of the Moon’s 29.5-day cycle.
Try to view the daytime Moon every day or two if possible. In just a few days you’ll start to develop a sense of its movement. Since the Moon orbits around Earth’s equator, it appears to travel nearly the same path as the sun; rising in the East and setting in the West. It rises and sets about one hour later each day so if you’re tracking it from day to day, keep that in mind.
Each time you see the Moon in the daytime sky, use one arm to point to the Moon and the other to the Sun. Take note of the angle your arms make. If you watch through the day, you should notice that the angle stays the same even as both the Sun and Moon track across the sky.
After a day or two, you’ll see that the angle between them has changed. Right now the Moon is waxing—each day it will seem a little larger as it moves around in its orbit so that we see more and more of the part that’s facing the sun. During these next few days, the angle between your arms will grow larger and larger.
Once you get a feel for this, we’ll build a model to see how it looks from space.