I like all the answers above. One possible method would be to build an envelope around the moon. This is an alternate to giving the planet an entire atmosphere, which it would periodically lose and need replenished, but it's still a gonzo engineering feet and the envelope would be subject to regular meteor strikes and punctures. It would need regular repair, or perhaps, some self repairing technology and leak plugging - that's no simple task.
Another method, which I like, would be to dig a very deep hole into the moon and have a kind of deep underground dwelling, with big fans to enable circulation and mirrors to reflect in sunlight.
As an earthly example, the Dead Sea is some 400 meters below sea level and as a result, it's atmosphere is about 5% more pressure. Source. On the Moon, with 1/6th the gravity of Earth, well, calculating it gets ugly, but if you dig a hole, some, 30-50 miles into the Moon's surface, perhaps at a steep incline to avoid direct sunlight but still take advantage of reflected sunlight. It might be possible.
Something, kind of like this but about 500 or 1,000 times bigger.
The hole or whatever you call it (Atmosphere well?) should requires far less replenishment of atmosphere than the surface terraforming idea. There would still be some, you'd need a light atmosphere around the entire moon to avoid too much loss and preserve most of the atmosphere in the deep hole, but it's more feasible than making the surface habitable.
Another alternative, with enough energy would be to generate to Oxygen directly from the silicate material of the moon, so the oxygen would be generated from within the hole.
Digging deep into the Moon might provide water sources and other minerals as well. I'm not sure anyone would want to live in a hole, but it beats living in a pressurized suit, never going outside.