As far as ancient Greek and Roman philosophers and through parts of the Middle Ages, the common theory for a long while was found in Plato's Timaeus, so I'll talk about that.

First of all, it stated the Moon along with the other heavenly bodies (the bodies visible from Earth to the naked eye - Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn in that order) orbited around the Earth in a circular orbit with the Earth as the center of the solar system. Now this didn't fit with the astrological charts and data gathered by the Babylonians, who kept charts of the visibility of planets and the orbits of the heavenly bodies for hundreds of years. This Plato acknowledged and put to his students, so that they may expand his system. The model would later be improved in Claudius Ptolemy's Almagest and Tetrabiblios and in multiple works of Eudoxus, who were some of the first to propose that the Earth was not the center of the known universe and that the planets may have asymmetrical orbits.

Next, the Timaeus covers the substance of the four elements, which were understood to be earth, water, air, and fire, in order of most dense to least dense, based on their composition. Specifically, they were each made of one of the four Platonic solids (cube, icosahedron, octahedron, and tetrahedron respectively) and because of this they were able to sort themselves into intermingling layers that started at earth and then rose upward until it hit the layer of fire, which we can think of as a sort of atmosphere. Now this layer of fire was thought to stop right when the orbit of the Moon began (imagine the moon's orbit as its own ring or layer), and then everything from the moon on was made of Aether.

According to Plato, Aether was defined as having no properties of the other four elements (not hot nor cold, not wet nor dry), which really meant no properties at all, and was thought to have no form or mass. It was thought to have come first from the Creator, a being that set the universe in motion by creating the Aether and the surrounding heavenly bodies, and then the four elements followed in layers to form the Earth. (Note: Some of this may be missing from the PG translation, I used a better one in my class but I can't find it for free. Apologies!)

While the four elements were affected by varying levels of gravity towards or away from the center of the earth based on their individual densities (the earth layer was the most dense so had the lowest gravity, and was closest to the center of the Earth), things made of Aether only had "gravity" that pulled them in circular orbits; since they were neither lighter nor heavier than the layer of fire, they did not move closer or farther form the center of the Earth.

So to recap: The Moon was the first heavenly body that followed the ring/layer of fire surrounding the Earth, but the Moon and its surrounding orbital path itself was made of a layer of Aether, a formless non-substance that would only move in a perfectly circular orbit around the Earth.

There was no "common theory". Different societies throughout time had different ideas about the universe. People in China in 2000 BC probably didn't believe the same thing about the moon as the Inca.

It's important to keep this in mind.