The advantage of being at the pole of any object in space where there is a low degree of inclination to the orbital plane around the sun is you can build a tower to reach up to the continuous light. This feature boosts the efficiency of your solar panels to 100% all year round which is vital to staying anywhere near the poles in the dark of winter. It also vastly simplifies your power storage for nighttime as well as the design of anything you want to stay pointed at the sun.
The moon is inclined with respect to the sun only 1 degrees 32 minutes. This is a very slight inclination and with an average radius of 1738 km you do not have to reach up high to be out of the shade.
The formula of calculating how high your tower has to be is as follows
Height = Average radius * (1/Cos(Inclination angle) - 1)
For the moon with a radius = 1728 km and inclination = 1.54 degrees this works out to be about 624 meters. On earth you would be looking at a major structure because you don't want it to come crashing down in a storm. The moon doesn't have storms so your need for overbuilding for wind factor is eliminated. Because the gravity is roughly 1/6 that of earth, your height can be roughly 6 times higher without changing the size of the structural members.
So what you would be designing for on earth is a structure 100 meters in height and then stretch it out to six times as long. This is equivalent to a 30 story tower which is smaller than many modern windmills.
There are three types of designs. The first is a traditional tower design that is fixed and all of the attachments to it like solar panels are fixed too. The problem for a polar tower is the only really good spot is the top one where you can pivot 360 degrees without hitting anything. The rest will have a moment of being in the shade of the tower if that matters. This design is well suited for multi function towers.
The second is where the whole tower rotates with the sun. The base is founded on a series of concentric train tracks that distribute the weight. If you add to your tower, you just add more wheels or add a new concentric ring for a wider base. This system greatly simplifies the tracking of the sun and makes it easier to focus everything in the same direction. Really big Solar Furnace arrays can be built that are fixed in the structure and you only have to move the focal point a bit. Additionally only one pivot connection needs to be made for electrical or plumbing connections which cuts down on maintenance costs. This design is well suited for power generation only towers where little activity is done after they are built.
A third type of design is a tower with the solar array that does not rotate but the top of the tower points to the sun like a sunflower does. The advantage of this type of tower is that the movable joints needed to make the tower bend this way are just hydraulic pistons substituting for some of the vertical/diagonal structural members. This type of joint can be lubricated to maintain a linear seal by encasing the entire length of the hydraulic piston in accordion fold type sleeve that holds a pound per square inch or so of gas pressure around the hydraulic piston so the lubricant does not evaporate. The same can not be done for the rotary bearings of wheels which are at the base of the second type of tower design. A thin foil accordion-fold micrometeor shield can in turn protect the pressure retention sleeve.
Another detail is the siting of the tower. The natural cratered terrain of the moon is thought to include a few peaks that are permanently in the sunlight. Siting a tower near one of these will significantly decrease the height needed to be in 100% year round sunlight. Additional towers will have a relatively minor effect of shading each other and can be built all over the poles of the moon until about 2 degrees from the pole where the height requirement gets up into the 3-4 km range.
The simplest method for assembly is similar to the terrestrial building cranes obvious on the skyline of most cities. These are module based systems with a crane at the top for lifting things into place. On earth these can reach to 30 stories easily so very little needs to be changed in their design to adapt them to the moon or elsewhere.
The process would involve the robotic or manual assembly of structural units by welding together nickel-iron structural members. Without carbon, these will be softer and more malleable than the higher quality steels on earth. Each unit is then lifted into place by a specialized crane attached to the rising tower. This crane would attach the unit by welding it to the tower then advanding the same height as the structural unit to be ready for the next on. Given sufficient supplies of nickel-iron and you could conceivably build a tower in only a few months. This is an important detail because you have have 6 months of continuous sunlight at the pole if you arrive at the spring solar equinox. If you get your tower up to a suitable height by fall then you will not have the problem of lack of sunlight during the winter.
Asteroids have a significant problem of being really cold. If they possess usable building materials like iron dust then building a tower may be the best way of solving this problem. The greatly reduced radius and micro gravity will likely make up for the lack of a better inclination. If you can build a really tall tower of several kilometers, you would be assured of a steady power source in what is otherwise a forbidding environment.