Reiterating what Cobragon suggested, the manual is a good option. But it doesn't communicate much about the game itself - more like he controls of how to work the game and the mechanics.
If you want to know the actual storyline of the game, you could search up and look through one of the many Pokemon X and Y walkthroughs on the internet.
Since X and Y was released very recently, a brief storyline of the game isn't available on Bulbapedia, unlike all the other games that has one that Bulbapedia provided. Sooner or later, one will be available, but for the time being I'd just sit with the walkthroughs. Plus, if you encounter a good walkthrough, you can encounter some items that you wouldn't bother looking for normally.
Hope I helped. :)