The main problem with installing an atmosphere is that the escape velocity of most of the gasses would be lower than their kinetic velocity due to the temperature required for a living environment (the main reason there is practically no helium, the second most common element in the universe; it's all leaked away, and all the remainder has been generated by radioactive decay). Thus, slowly, the air would escape into space, and after a few tens of thousands of years will become too thin to support advanced life.
You could add a few megatonnes of volatiles by crashing a comet against it. If you brought it in the right angle you could perhaps break the tidal lock, and add some spin, possibly reducing the extreme temperature variations between day and night; if not you'd need some mechanism to equalise the temperature between day and night regions, perhaps a superconducting grid covering the entire surface. If you relied on atmosphere to transfer the heat you'd get continuous hurricanes, eliminating all hope of personal flight and most of outdoor agriculture. And if you put giant mirrors behind the moon, reflecting the sun back onto the dark side, the overall temperature would be too high, as the moon is in the same orbit as the Earth (perhaps if you orbited the mirrors they could reflect away a portion of the brightside energy, and balance out the equation).
A force field to maintain the atmosphere, as in Heinlein's 'Farmer in the Sky'? I don't like anything that makes the survival of an ecology dependent on technology. Oh, you can say that a major power cut would kill thousands of people, that the collapse of the water pumping system tens or hundreds of thousands, but nothing would endanger the overall environment more than we're doing already.
A very big plastic bag round the entire satellite? Not only would the amount of mass required be enormous but the constant impact of meteors would render it useless after less time than the leakage due to low gravity.
Better to build a few hundred Australia sized giant domes on the surface, with orbital speed trains between them. Easier to mend, big enough to fly in, and you can start small and build up. Of course, the existence of a sizeable population means you can't crash a comet into it; the moonquakes, the shockwave from installing an atmosphere, the gales stronger than a hydrogen bomb explosion all render the exercise inadvisable. And, if you have to silver the domes to avoid the heat loss during the dark period you lose your romantic Earthlight and non-twinkley stars.
Sorry.
