Well, obviously you wouldn’t have open fields and wooden houses and things like that; the most likely method of colonization would be vacuum-sealed settlements, possibly even whole cities, although they’d be nothing like the cities you or I know. Of course there’s also the problem of severe radiation from the lack of atmosphere on the moon, so another likely option would be to build subterranean settlements under the moon’s surface.

Also, from my understanding we could’ve had a moon colony decades ago if it were not for capitalism.