Pressing the Build button will open the Planetary Structures Building screen. From here, you may build structures on the planet, such as mineral mines , factories and defense posts. The maximum number of each that can be constructed on a planet is dependent on the colonist population. More information on how to actually build these structures can be found here.
The cost of each structure is as follows:
Structure Supplies MegaCredits Mineral Mine 1 KT 4 Factory 1 KT 3 Defense Post 1 KT 10
Mineral mines extract minerals from the planet. Each factory produces 1 KT of supplies each turn. Defense posts help protect a planet from attacking enemy ships and ground troops.
When there are not enough colonists on the planet to maintain structures on the planets surface the structures will decay at a rate of 3 structures per turn.
Additional details can be found here.