Building things in the Belt has been an exercise in making use of available materials. Wood is expensive, because it's rare and time-consuming to grow. A lot of typical construction processes from Earth before it went dark simply aren't options. What we've got to work with are stone, metals, and "plastics" created by bio-engineered micro-organisms.
Since a lot of the asteroids in the Belt have metals, and most of them are stone, it should come as no great surprise that most of the structural bones of constructions in the Belt are made of stone and metal. The specifics of the stone vary a lot based on what's available on any given asteroid, but generally fall into one of several typical silicate mineral classes.
Though it's technically possible to sustain extraction of stone for construction purposes for a long time, it's generally more efficient for construction purposes to have standard stone-block units that can be re-used when necessary. These units are roughly shaped like Lego® blocks, though much larger and quite a bit heavier. They may or may not be secured to each other with a dissolvable adhesive, though in most cases it's not really needed — a “dry fit” is generally sufficient in almost all cases. These blocks also provide a substantial amount of thermal mass, which helps keep temperatures in a livable, comfortable range for humans. These blocks are commonly used for “interior” walls, and are typically made with a variety of “peg-holes” that can be used for standard plastic or metal hooks, pegs, and shelves, to hang things on the walls.
Most of the time, though, since humans need air-space to move in, construction on an asteroid is mostly a tunneling/digging effort: cutting out enough stone from a given area to provide space to move around in. A fair amount of effort goes into making those spaces reasonably rectangular, since even in the microgravities of the various asteroids, that's what people were used to. That said, insulation between the native rock and the livable spaces is still needed, so it doesn't need to be terribly accurate — Usually, this is a foamed “plastic” material.
There's a fair amount of metal available in the Belt, particularly nickel and iron, but nowhere near as much as raw stone. Construction use of metals is generally prioritized around ship-building and environmental-control needs: It's pretty much impossible to build an airlock from something other than iron or steel, for example.
Metal wall-framing with some sort of plastic wall-sheeting is not unheard-of, but is atypical in residential areas — the advantages of the modular wall-blocks are significant.
True plastics, being petrochemical derivatives, are pretty much impossible in the Belt, where there have been no geo-chemical processes — or available bio-matter, really — for the raw petroleum to form. That niche has been largely filled by a variety of bio-plastics, created from a material much like cornstarch, and some other chemicals that are easily manufactured, even in the Belt. In the last 20 years or so, there's also been significant development by the Company in developing micro-organisms that will generate a very similar material, given little more than water and some kind of organic material.