Pokémon X and Y Walkthrough, Pokémon Move Sets: Vaporeon
(Please note that the recommendations below are largely made for in-game play. A Vaporeon in a competitive environment will likely make use of different moves to accommodate for smarter, more adaptive opponents. If you've got a different Vaporeon build that you'd like to share, the comments are waiting for you.)
One of the three original Eeveevolutions, and possibly one of the most-overlooked because there's already a glut of water-types on the market, Vaporeon means business. It may look friendly, and perhaps even a little fragile, but this defensive water-type can beat down the strongest opponents and live to tell the tale.
Vaporeon famously begins life as a fuzzy little Eevee. You can evolve it into a Vaporeon by giving it a Water Stone.
Fire, Ice, Steel, Water.
Vaporeon's lithe form hides a surprising secret: its HP base stat is enormous. It can almost always survive at least one attack, as it never has to worry about a quadruple weakness. Its Special Attack is almost as monstrous as well, with Special Defense coming in third. Attack, Defense, and Speed all clock in at a little below average.
Water Absorb: If the pokémon is hit by a water-type attack, it will absorb the damage as HP. Water-type moves are relatively common, so switching into Vaporeon when you know one is coming is a good way to surprise an enemy. Nevertheless, this is not that great an ability, since most baddies will know better than to target your Vaporeon thusly.
Hydration: If the pokémon receives a status ailment while it is raining, the ailment will be cured immediately at the end of the turn. Hydration is much more useful than Water Absorb, as it allows Vaporeon to use Rest in conjunction with Rain Dance to completely recover its ample HP without having to worry about sleep. Hydration is a hidden ability.
There are two general routes you can go with your Vaporeon. The first is that of a wall. Start with either Surf for outstanding STAB superiority or, at a slightly lower attack strength but probably better overall impact, Scald. The latter stands a good chance of burning foes. Follow this up with two or three non-STAB moves to cover a lot of ground (I like Ice Beam and Shadow Ball, personally) and something to keep Vaporeon healthy, such as Aqua Ring, to finish off your pokémon.
Alternatively, you can make your Vaporeon into a staunch, effective Toxic user. As with all Toxic-centric pokémon you should equip Vaporeon with moves that boost its survivability, and it has a lot. Aqua Ring coupled with Leftovers provides a steady supply of health; Acid Armor covers for Vaporeon's poor Defense; Protect, y'know, protects; Substitute is just generally irritating. You may also want to keep at least one offensive move, in which case I recommend Surf to maximize damage.
EV / Super Training
EV training depends on your build. A wall will want to pump 252 EVs into Special Attack while relegating the rest to its HP, its Defense, or a bit of both. A Toxic Vaporeon can forego Special Attack and focus its efforts on HP, Defense, or Special Defense. Given that Vaporeon's already going to have a substantial HP count, I'd recommend Defense and Special Defense.
Catching a Vaporeon
Vaporeon to not appear in the wild. To get one you'll need an Eevee, and the best place to find them is on Route 10. Check the yellow flowers here to boost your chances of coming across an Eevee in a timely fashion.