I designed and built an experimental vacuum chamber...
That got down to ~10^-11 Torr with hard work
As for the moon: http://www.iac.es/galeria/mrk/atmo_lun.html
These experiments revealed that there is a very tenuous lunar atmosphere, which has a total mass of only about 10 000Kg (10 tonnes). Most of the atmosphere is made up of Hydrogen, Helium and Neon captured from the solar wind. There is also a component of gases from radioactive decay in the surface rocks: 10% of the Helium appears to come from alpha decay and 90% of the Argon (at 10000 atoms per cubic centimetre it is one of the major components of the atmosphere) comes from this source. Argon actually presents a problem because, given the known amount of radioactive Potassium 40 in the rocks, it requires all the Argon 40 produced from the decay of Potassium 40 in the top 5km of the lunar crust to be released very efficiently to the atmosphere to explain the amount of gas which is detected. Smaller amounts of Carbon Dioxide and Methane are seen, but the water vapour content of the atmosphere is negligible: around 0.5 molecules per cubic centimetre and that due to reactions of solar wind particles in the soil. Totalled over the entire lunar surface there is only around half a gram of water in the atmosphere.
Obviously, as water was one of the main gases released by the landings, the problems of contamination are very severe when determining the amount of water vapour, but it seems that the amount of water vapour released by outgassing from internal activity, or from ice at the poles is virtually zero. In contrast, Apollo 15 did detect what appeared to be a major release of radioactive Radon on one pass over the crater Aristachus.
One curious detail is that the lunar atmosphere is much denser at night (when it is cooler) and also the composition changes: the Argon condenses out at sunset and is only released again in the morning; the small amount of Carbon Dioxide also freezes out and there is a strong tendency for the atmosphere to migrate across the terminator from the day to the night side.
Studies have also revealed that the balance is very delicate. At present, the solar wind sweeps the lunar atmosphere into space very efficiently, limiting its density to that of a collisionless gas (an exosphere). If the atmosphere were, however, a factor of just 1000 denser, this process would invert itself and the atmosphere would remain stable for tens of thousands of years. Just the Apollo missions to the Moon increased the atmospheric density by a factor of 10 with rocket exhaust (mostly CHON compounds). Large scale human activity on the Moon could push the total mass over the limit and create an artificial atmosphere, pushing the Exobase off the surface and creating a stable, if highly tenuous atmosphere which could threaten precisely the most important asset that the Moon can offer us: its sterility and almost atmosphereless nature. There is even some evidence, from the lack of certain sizes of microcraters in surface dust that the Moon did have such an atmosphere in the past, perhaps as much as 10 million times denser than now.
Other references place the atmospheric pressure on the moon between 10^-11 to 10^-12 torr...
Achieving this in industry would be do-able but pretty tricky...