how and where to catch an Eevee in Pok'emon: X/Y

Where to catch an Eevee you may ask? Route 10.  This route is right outside of Cyllage City. I'd suggest while you're there, to challenge the gym leader, Grant.  There is a 5 out of 10% chance of finding an Eevee.  So keep running around until you find one.  Once you encounter this little fur-ball, if you have a Squirtle, use bubble twice, but if not, use a weaker pok'emon so the poor thing doesn't faint so quickly. I say this because the best time to catch your Eevee is when it's health is at least in the yellow area, but an even BETTER time is when it's health is in the red. This is because, sure when your pok'emon's health is in the yellow, it's weak, and you should use a potion if it's really that low but, the red is even better because it means the pok'emon is at it's weakest state. The weaker, the better, and another tip is to use a heal ball if you can, but if not, like stated earlier, route 10 is right outside of a town so after adding this little guy to your party, you can heal it right up at the pok'emon center. 

Some may know that Sylveon, the newest Eeveelution, made it's very first appearance in the short and sweet episode called, Eevee and friends. this episode was an extra in the movie, Mewtwo's return.  This movie came out about a year before the series Pok'emon, Black and White Univa Region came to an end. this gave GameFreak plenty of time to make the games, Pok'emon X and  Pok'emon Y.  Sylveon was added to this game. Some wonder how to get Eevee to evolve into Sylveon. The first thing to do is to make sure that your Eevee has at least one fairy type move. most of the time they already have learned the move, Baby-Doll Eyes. but you still need to check. Then it's time to spend hours playing with your new Eevee in Pok'emonAmie. Pet your Eevee, play with it, feed it, until its affection is at the highest stat.  When you gain a heart in the affection, Eevee will start jumping and it will have about 500 hearts come out. you know that the deed is done when Eevee jumps around in a circle many times with 10,000 hearts coming out. now it's time to level it up! the eevee may evolve at Lv.20 it all depends on the Eevee. Eevee should evolve around Lv.20 though. Again, it all depends on the Eevee. Good luck!