I'm a doctor, not a mechanic
This page is the hub for all things to do with the actual building of the Unreal world. Here, architecture is about creating an environment for players to move about in. Here on the Unreal Wiki we've pretty much split the topic between technique (this page) and design (Map Design).
Prior to UT2003, all architecture was made with CSG in UnrealEd. This treated the Unreal World as a giant lump of clay, which the mapper then hollowed out with primitive shapes: the brushes. The build process then compiles a BSP from the brushes, and the mapper applies stored textures to the visible surfaces.
This method still exists in UT2003/4, but there's now an extra layer on top of this: static meshes. These are hardware-cached elements which add a tremendous amount of detail to a map at a relatively small extra processing cost. A static mesh is a saved resource, like a texture. They can be made in UnrealEd, but this is not optimal: it's best to use other applications.
Lastly, there is the terrain system, which is another thing yet again.
So making the Unreal world believable to the players boils down to three things: