There are two kind of constructions: buildings and stations. As your research progress, you will be able to construct more types of buildings and stations.
Buildings[]
Home Base buildings are constructed by technicians.
You must have certain level of specific resource to build a building, and construction happens one by one, by technicians assigned to Civil Engineering.
Stations[]
Territory stations are constructed by technicians or scientists.
To build stations, you must first assigned people to Technical Bay or Scientific Bay. Once you have placed a construction order, a suitable vehicle will be launche from the bay and head to the territory to do the construction.