To build towers first click on the one you want to build on the right, then click on the map where you want it to be built. If the selected place to build is not available. The tower image will turn red. If you change your mind pressing ESC will cancel your choice. But once build you can click on them to upgrade or sell. 

at the start of the game you will only have money to build Basic Towers. The first two types, but as the game prodresses you will have the gold pieces needed to build the rest of them aswell. They are increasingly more puweful but also expensive.