The process of making something from simple subunits is called?

In the case of making a house from bricks, it is called "building".

Perhaps the term "assembling" could also be applied and if you were to be making a polymer then polymerization would be the term to use. If you were assembling something using Words as sub units the process would be called writing or if you were a musician, composing. If you were a computer programmer then the process would be called coding.

This answer is probably not exhaustive.