Meant to post this one last week but I was busy.
In the process of becoming a spacefaring species, our moon is vital. As our nearest neighbor, it serves as a stepping stone to the solar system and beyond. Its size, (lack of) atmosphere, proximity, and composition make it uniquely suited for a variety of roles.
The first step in any of this, to truly utilize the moon, will require reasonably available transportation to and from. Advances across the board in space transport have made it far cheaper than previously, but this still isn't enough. For ease of access, either purpose-built orbital launchers capable of accelerating crafts to a lunar rendezvous without the use of expensive fuels or a lunar elevator will be required. A trip to the moon needs to be on par with a transoceanic flight, or at least a ride aboard a cargo ship, able to ferry people and supplies to and from Luna without a lot of fuss and bother. These options, and specific details of their design, development, and implementation, will be discussed some other Wednesday.
Now, to get one thing out of the way: As soon as lunar colonization because feasible, there will be massive hue and cry to preserve the moon, with laws and treaties and threats of war if anybody does anything visible on the near side of the moon's surface. This is less of a hindrance than it seems, owing to the fact that the other side of the moon still gets decent light, and the fact that the moon has no atmosphere for breathing or protection.
The moon will be one, or more likely a series, of arcologies. Every last cubic inch of habitable space, and a great deal of the unhabitable space, is going to have to be put there manually. Much of it will be below the surface, to shelter from the otherwise unblocked cosmic radiation and space debris. The moon is, however, incredibly dense and contains a great deal of ore, which will be used in the colonization effort.
At 1/6th of Earth's gravity, even assuming things are made otherwise habitable for regular life, the human body will require assistance to maintain itself. At its simplest, clothing will be made featuring resistance bands to make the body work as if it were subject to gravity. Depending on advancements in technology, such things as the recently developed sonic tractors may be used to increase downwards force to create artificial gravity, or even rotational artificial gravity in the manner of a graviton. Still, this is of great use for functional industries such as shipyards.
One of the primary purposes for the lunar sites is to serve as starports. Ships that wouldn't be able to escape Earth's gravity and atmospheric resistance can be built, launched, and landed on the . These ships will open reasonable transit times to the farther reaches of the solar system, even with current propulsion systems.
Another benefit of the moon is easier orbital training. With less gravity, setting training facilities, orbital shipyards for craft too big even for lunar production, and so on into orbit can be done at much nearer to the planet and safety via escape pods or similar. Specific details of orbital stations will be discussed in a separate post.