Pokémon X and Y Walkthrough, Pokémon Move Sets: Gardevoir
(Please note that the recommendations below are largely made for in-game play. A Gardevoir in a competitive environment will likely make use of different moves to accommodate for smarter, more adaptive opponents. If you have a Gardevoir with a different setup, let everybody know how cool it is - and why! - in the comments.)
Sporting a chique hairstyle and a lovely dress, Gardevoir has become one of the staple psychic-types since its introduction in the third generation. Not only has it been graced with an alternate evolution in Gallade, Gardevoir itself is the recipient of a Mega Evolution in the sixth generation. This fact alone has turned it into a constant competitor in the online world of Pokémon X and Y... and gaining fairy-type status doesn't hurt either.
Type: Psychic / Fairy
Gardevoir begins life as a tiny, innocuous Ralts. It will evolve into a Kirlia after being leveled to 20, and further leveling to 30 will net you a Gardevoir. Keep going by attaching a Gardevoirite and you'll get Mega Gardevoir.
Fighting, Psychic. Immune to Dragon.
Ghost, Poison, Steel.
Gardevoir is fairly similar to its psychic-type contemporary Alakazam, though with a bit more emphasis on survivability and less on being a glass cannon. As you might expect Gardevoir's greatest stat is Special Attack at a mighty 125, followed close by Special Defense at 115. Speed clocks in at an average 80, while everything else is a below average 65. This can be a little worrisome, as Gardevoir becomes an obvious target for pokémon that sport physical attacks... like, oh, steel-types.
Gardevoir doesn't change as radically as you might hope when turning into Mega Gardevoir. Its Special Attack and Special Defense both get huge boosts, true, but its HP and Defense both remain pretty much the same. Oh well. Speed gets a decent jump, though, so Gardevoir becomes a more viable sweeper.
Synchronize: If the pokémon is hit by poisoning, a burn or paralysis, the opponent will receive that same status ailment. This is handier on other pokémon with more HP, as Gardevoir's opponents are more likely to go for a straight kill. Still, not terrible.
Trace: The pokémon copies the ability of the opponent. Very gimmicky, this, and the effects can range from fantastic to downright detrimental. Not recommended.
Telepathy: The pokémon is protected from attacks used by an ally in a double or triple battle, such as Earthquake. Good if you engage in such battles regularly; otherwise useless. Telepathy is a hidden ability.
Pixilate: Normal-type moves change into fairy-type moves instead, thus receiving a STAB boost. Absolutely fantastic if you like to give Hyper Beam to your Gardevoir. This ability is only available to Mega Gardevoir.
Gardevoir has the makings of a fairly standard sweeper, even with its slightly lacklustre Speed stat. Consequently, most Gardevoirs will have a stacked set of attacking moves. Psychic and Moonblast cover the STAB bases, while Thunderbolt, Shadow Ball, Focus Blast and Energy Ball all provide outside coverage. I recommend Focus Blast in particular for warding off steel-types, but that's just me. If you want you can also toss in Calm Mind to increase Gardevoir's damage output, though delaying a turn to use it can be risky. Consider replacing Psychic with Stored Power if you opt for Calm Mind.
Gardevoir can also work decently well with a few supportive moves. Will-o-Wisp is a favourite, as it offsets some of the damage done by physical moves when it lands. Hypnosis and Dream Eater are possibilities if you want your Gardevoir to last longer than a single battle, or just Hypnosis on its own if you don't care about healing your Gardevoir. Whatever your choice here, make sure to have at least one STAB move, preferably Moonblast.
As for Mega Gardevoir? The above suggestions all remain solid, though you'll want to include Hyper Beam. It's just too awesome when paired with Pixilate. Make sure you save it as a round ender, though - that missed turn can be fatal for your Gardevoir.
EV / Super Training
Gardevoir as a sweeper needs all the Speed it can get, so start there. Beyond that you should concentrate on Special Attack for bolstering Gardevoir's OHKO capabilities. If you're looking for a slightly more gimmicky Gardevoir with supportive moves, transform it into a special wall by beefing up its already considerable Special Defense or HP in general.
Catching a Gardevoir
Gardevoir itself can't be caught in the wild. Fortunately, it's not that difficult to track down its predecessor, Ralts. You can either find it on Route 4, or, if you wait until after beating the game, you can trade for one from the champion. She's waiting for you in the same cafe where you met her in Lumiose City. This Ralts will also have the Gardevoirite needed to evolve into Mega Gardevoir.