Not all buildings and objects can be stored. If this is an option, you will see a blue box when tapping on a certain object:
 
 
Currently, you have an option to store the fire pit and some decorations.
NOTE: Active (charged) decorations that still give bonuses can't be put into storage. You will be able to store them once you have used up all the available bonuses.
If the decorations were obtained during a Farmer's Season, you will have to wait until the Farmer's Season is over to be able to store them.
 
Where can I find stored objects?
To find the objects that you previously stored, open the construction menu (the helmet in the bottom left corner of the screen) and go to the tab with the box icon: