I have used images from the east-facing HPWREN camera at the Mount Laguna Observatory to show how the Moon's position in the sky changes as it moves through its orbit. A plot showing the apparent position of the Moon every 24 hours and 50 minutes for 1 month is called the Lunar Analemma.
It takes a bit less than 24 hours for the Earth to spin once on its axis, and in this time the Moon moves around the Earth. So, on average, you need to wait about another 50 minutes for the Earth to spin a bit more for your side to face the Moon again, but the timing is different each day. The exact amount of extra time you need to wait depends on how fast the Moon is moving in its elliptical orbit around the Earth. When the Moon is closer to the Earth it moves faster, and when it is further away it moves slower. So sometimes the Earth needs a little more or a little less time to face the Moon again. If we look at the Moon every 24 hours and 50 minutes, we will notice the moon appears East of where it was before if it is moving faster than average or West of where it was if it is moving slower than average.
The Moon's orbit is also tilted compared to the Earth's spin axis. So sometimes the Moon is south of the Earth's equator, and sometimes it is North. As viewed from Earth, this produces the north-south motion in the Lunar Analemma.
The shape of the Lunar Analemma changes with time. Some months the shape resembles a figure 8, but the crossover point in the middle can slide to the southern or northern limits resulting in a more paddle-shaped loop. This change is due to precession of the Moon's orbit--the axis of revolution and the direction of the orbit's major axis both change over time due to the gravitational pull of the Sun, Jupiter, and other objects in the solar system.
In the video, I mark the position of the Moon in each image with a green circle. These circles are always larger than the apparent diameter of the Moon, although sometimes the Moon is over exposed and the glare around the Moon might make it look bigger. I shade these circles to indicate the phase of the Moon. The Moon can be difficult to see when it appears closer to the direction of the Sun. Notice that this always occurs when the Moon is in its crescent phase.