There are three ways of obtaining a building in Populous.

 

Firstly, if you have that building unlocked, you will start the level with it. Online, if that building is avaliable in the restrictions, every player will be able to use it.

 

Secondly, worshipping a vault of knowledge in the campaign will unlock that building permanently. This is the main way of obtaining buildings when playing the singleplayer.

 

Finally, worshipping a stone head can give you a shot of a building - when this happens, you can only build that building once, and only in that particular level. Only vaults of knowledge unlock buildings permanently.