How do you move a building?

You can move buildings that you have placed (not the main ones though). To move them you actually need to Remove (demolish) it and then build it again.

To on the building and then tap the small hammer icon in the top left of the buildings info screen. This will show you the remove options. Removing it will take time depending on the level and use a build queue but you can also pay diamonds to remove immediately. Once done you can place the building again in the new location.