Question

How to get Float Stone?

Answer 1

On the odd occassion in battle, you will notice various things in the background, ranging from trees in the field to rock formations in caves. These seemingly inocuous background objects do have a specific function, they can be destroyed and cause you to receive an item.

The Float Stone can be acquired by destroying background boulders using the move Rock Slide in various caves and routes.
this is what you should look for while battling wild Pokemon (the big rock in the background):

Source: http://www.serebii.net/itemdex/floatstone.shtml

                 http://www.serebii.net/xy/wilditems.shtml

Answer 2

Natural objects are a game mechanic
introduced in Pokémon X and Y. In both wild and Trainer battles, they
can appear behind the opponent. These objects can be hit by specific
moves that would hit multiple Pokémon (even if used during a single
battle). If they are hit, they break or drop Berries and remain that
way until the end of the battle, when the player will pick up one
item. If a natural object can appear, a platform will be visible
behind the opponent; any natural object will appear on this platform.
Only one natural object can appear at a time, and once it is broken it
remains broken until the end of the battle. The item is picked up
after the player's Pokémon have gained experience from defeating the
last Pokémon. The player will not be able to pick up the item if they
lose, run, or catch the Pokémon.

The Float Stone can be obtained the same way
You will have to battle at Spiky Rock 1 which can be located in the Connecting Cave, The Sea Spirit's Den, Terminus Cave, Victory Road(internal) and the Unknown Dungeon. In order to trigger it you must use Rock Slide or Hyper Voice in a battle with a Pokemon and you must not catch or run away from the battle, you must defeat it.
You will need a little patience with this because there is also a chance of encountering the Hard Stone.

Answer 3

It can be found in random boulders in battle. No other way.