Construction units are what actually gets your army up and running from scratch. The main units are called Engineers, which come in three different tech levels, differing for building speed and array of available building choices. So, a T3 Engineer can build T1 structures as a T1 Engineer, but much faster. Other construction units include the Armored Command Unit, which starts with a limited building choice (less than a T1 Engineer) but slightly higher building speed, and can be upgraded, and the Support Command Unit, which can also be upgraded and already can build T3 structures. T3 construction units, SCUs and (upgraded) ACUs can also build Experimental units.
Construction units (and military units that have a limited Engineering Suite, such as the Mantis T1 Cybran Assault Bot, and the Aeon T3 Harbinger Siege Bot) can also assist construction of structures and units with the Assist (I) command, speeding up the process at an added Mass and Energy cost.
Units with an engineering suite can also reclaim destroyed units and structures and repair friendly structures and units. Oddly, the Cybran Mantis is unable to reclaim destroyed units and structures, however the Aeon Harbinger can. If an engineer, ACU or SCU (but not Mantis or Harbinger) is ordered to patrol an area with reclaimable mass in it, it will automatically harvest that mass.
Also, if ordered to build a structure over an identical wreckage, the build procedure will start from 50% (so, if you build a T1 Point Defense over the wreck of a T1 Point Defense, its construction will start from 50%). This means that often it's more efficient in terms of time to not reclaim something like a Point Defense, and build on top of it again instead (however, reclaiming the wreckage will typically yield more mass).