The Everstone can be found in Pokemon X and Y in Geosenge Town from a lady northwest of the Pokémon Center. See here for a video.
Multiple Everstones can be given to the player from the Psychic Inver after an Inverse battle on Route 18. After defeating the Inver, if none of the player's Pokémon fainted, he will give the player three of the same item from a selection of several. If the player's Pokémon fainted, he will give the player one item from the same set. The Inver can be battled once per day.
An Everstone also has a 50% chance to be held by wild Roggenrola and wild Boldore when caught.
Hope I helped :)