Structures are built within your Ship on the pads provided, and are used to spawn units, summon god-beasts, heal and revive. Each implies a mineral cost and a short building time.

To build a structure, select one of the pads by tapping on it, then choose the structure from the list of icons at the bottom of the screen. Then, press the Build button to the right to start building.

You may only have one structure of each type, and also only one God-Beast altar at a time (so you can't have a fire and an earth altar at the same time).

Also while in the Nightswan, you will have listed in the top screen all the Waiting Skills that your characters are providing, which can affect cost of structures, building time, or unit spawning time.