Each building info card features the cost of and term (days) of construction.
Before starting a construction, make sure you have enough money. Click on the building info card. If you want to build several constructions of this kind, press the card image and hold it (some devices may require you to swipe in order to queue several constructions).
Upon construction completion, you will see a notification. Notifications of this type can be turned off on the settings screen.
You cannot cancel construction or demolish already existing buildings.