Select the Store Building item from the inventory. You will then be shown the view of your city. Buildings which can be stored will have a special symbol above them (a star, I believe). Click on the building which you wish to store and it will give you a confirmation prompt. If you choose yes, the building will be stored in the inventory. Remember that it will still be of the age in which it was won and will not upgrade.
In case you do not have a "store building" item, you have no option to save a Special Building. Also, regular buildings, premium buildings and great buildings (everything available from the build menu) cannot be stored at all.
AFAIK, "Store building" items can be won in Events and in the Guild Expedition and rarely in the Daily Challenges.
It would be nice to be able to store Premium Buildings, since you get nothing back if you nuke them, and they cost diamonds (or in rare instances are won) and this has a cost to the player.
It is a different circumstance than the other bldgs from the menu!
I already made that suggestion in the forums some time ago.
On the other hand - should you really decide to remove a diamond building from the city, it is because it is outdated and its stats are just not worth it anymore. So the only reason to store the premium buildings would be to sell them to the antiques dealer...
Another route, then, would be able to sell that building right off your city street and into the dealer’s arms. Another would be to make the building upgradeable to the current age, w increased output.
What do you think?