In the centuries after Galileo's discoveries, the Moon was extensively studied by astronomers using telescopes. One thing soon became clear: it had no atmosphere. When a star was eclipsed by the Moon, it vanished suddenly and its light showed no refraction or absorption by an atmosphere.
Why? By the laws of motion, the Moon orbits not the center of the Earth, but the center of gravity of the Earth and Moon (this is discussed at http://www.phy6.org/stargaze/Skepl1st.htm#q201, and the center of gravity is defined in http://www.phy6.org/stargaze/Srocket.htm). The location of that point allows astronomers to deduce the mass of the Moon, and from that, the pull of the Moon's gravity. At the surface of the Moon, it turned out, gravity is only 1/6 as strong as at the surface of the Earth.
Gravity is important for the retention of an atmosphere. It holds an atmosphere down, while heat is what can make it escape.
Heat is related to atomic or molecular motion. In solids and liquids, atoms or molecules can vibrate around their average position. The higher the object's temperature, the more vigorous the motion, until the material boils or evaporates, at which point its particles shake loose altogether. In a gas atoms and molecules fly around randomly, colliding constantly (if the gas is as dense as it is in the atmosphere), and their collisions lead to a very good explanation (“the kinetic theory of gases") of the observed properties of a gas.
The average velocity of a gas molecule depends on the temperature of the gas, and at room temperature it is comparable to that of the speeding bullet, quite below the “escape velocity" needed for escaping Earth's gravity. However, that is just an average: actual velocities are expected to be distributed around that average, following the “Maxwellian distribution" first derived by James Clerk Maxwell, whom we meet again in the discovery of the three color theory of light (http://www.phy6.org/stargaze/Sun4spec.htm#q1C) and the prediction of electromagnetic waves (http://www.phy6.org/stargaze/Sun5wave.htm#q38A). According to that distribution, a few molecules always move fast enough to escape, and if they happen to be near the top of the atmosphere, moving upwards and avoiding any further collisions, such molecules would be lost.
For Earth, their number is too small to matter, but with the Moon, having only 1/6 of the surface gravity, it can be shown that any atmosphere would be lost within geological time. The planet Mercury, only slightly larger, also lacks any atmosphere, while Mars, with 1/3 the Earth's surface gravity, only retains a very thin atmosphere.
Water evaporates easily and once in gas form, is quickly lost by the same process. That suggested the “maria" could not possibly be oceans, though their name remained. They actually turned out to be basaltic flows, hardened lava which long ago flowed out of fissures on the Moon; no present-day volcanism on the Moon has been reliably identified. The vast majority of craters probably date back to the early days of the solar system, because the lava of the maria has very few craters on it, suggesting it flooded and obliterated older ones.
The picture of a dry Moon was reinforced by Moon rocks brought back by US astronauts. Earth rocks may contain water bound chemically (“water of hydration"), but not these. Water, of course, would be essential to any human outpost on the Moon. Yet small amounts of water may still exist, brought by comets which occasionally hit the Moon. All this water is sure to evaporate in the heat of the collision, but some of it may re-condense in deep craters near the Moon's pole, which are permanently in the shade and therefore extremely cold. Observations by the “Clementine" spacecraft suggest that one such crater may indeed contain a layer of ice.