Step 1: Teach your Eevee a fairy type move. (I don't know if has to be Baby-Doll Eyes though XD)
Step 2: Play with Eevee in Pokemon Amie in till it has max affection. :D
Step 3: Train up Eevee but try to avoid places with the ice rock and moss rock..
Step 4: Enjoy your new Sylveon! :D