xy Pokemon Raising
Introduced in Pokemon Gold and Silver, breeding has become the bulk of both post-story gameplay for every game that's followed. A perfectly-raised pokemon is more effective in battles against your friends and fellow competitors of competitions and though it used to take a long time to get one of those perfect battlers, Pokemon X & Y have streamlined the process considerably.
The basic information you'll want to first know are Individual Values (IVs), Effort Values (EVs), and Natures.
Individual Values
A pokemon has 6 IVs that correspond to its HP, Attack, Defense, Special Attack, Special Defense, and Speed. These can range anywhere from 0 to 31 and you can see that difference completely at level 100 meaning a Pokemon with 31 HP IVs will have 31 more points of health than a pokemon with 0 HP IVs. These are determined at the generation of a pokemon, either when first encountered in battle or when an egg is given to you to hatch. They cannot be modified in any way.
You can breed certain IVs through trial and error with one parent holding the Destiny Knot, an item that guarantees that 5 out of the 12 IV numbers (6 from each parent) pass down. Basically, just keep breeding and replacing the parents with better IV'd offspring until you get the desired result.
An easy way to start off the process is with pokemon from the Friend Safari as any encountered there will have at least 2 of their IVs at 31 when encountered every time or with pokemon that can't breed but evolve into ones that can (Riolu, Azurill, other Baby Pokemon) as they have 3 of their IVs at 31 when encountered in the wild.
Both the Friend Safari and the IV checker, an NPC in the pokemon center that tells you a pokemon's highest IVs and the summary of the total IV count, are found in Kiloude City. Make sure to look for the "can't be beat" message as that means the IV is at 31.
Effort Values
EVs are ways to enhance these 6 stats further (HP, Attack, Defense, Special Attack, Special Defense, and Speed). EVs can be obtained in the following ways:
Step One: Vitamin drinks:
HP Up - HP
Protein - Attack
Iron - Defense
Calcium - Special Attack
Zinc - Special Defense
Carbos - Speed
Each Vitamin drink adds 10 to that stat's EV total and can only be used until that stat's EV total becomes 100. Basically, use these drinks first.
You can only have 510 total EVs and only 252 per stat meaning, most of the time, you'll max out 2 stats and have a 3rd get the remaining +4.
Step Two: Horde Battling:
After you've used the vitamins, you'll have 152 EVs left in your two main stats and 4 left in your third stat. You'll want three things:
1 - A pokemon with the move Sweet Scent and an attack that can hit an entire horde at once, like Petal Blizzard. Venusaur is a fantastic example.
2 - The pokemon you're raising holding the Macho Brace and under the effect of Pokerus, a helpful virus that you can randomly encounter (but should probably look for on some Pokemon forums). Pokerus passes during battles (have EXP share turned off and make sure the one you're raising is not in battle at all). Once your project has been infected, stow the infecter in the PC to retain the virus (Pokerus cannot be passed after a day if the pokemon is not in the PC).
Both Pokerus and the Macho Brace double the amount of EV's you get from battle meaning if a Pokemon gives 1 Attack EV after being defeated in battle, it'll be doubled to 2 then again to 4 if both the virus and brace are on your pokemon.
3 - EXP Share turned on, you get this Key Item after the first badge.
Now, Horde Battles are 1 vs 5 battles where you're the outnumbered one. Sweet Scent triggers these so long as it's not raining.
Have your Venusaur use Sweet Scent and you'll encounter 5 pokemon. Use Petal Blizzard to wipe them out. EVs share without any division so your entire team will get the full amount of EV's possible from the encounter. Below is a list of routes to choose for the stat you want to focus on:
HP - Route 5 - Gulpin (1 EV) x 2 (Brace) x 2 (Pokerus) x 5 (horde) = +20 EVs
Attack - Route 14 - Bellsprout (1 EV) x 2 (Brace) x 2 (Pokerus) x 5 (horde) = +20 EVs
Defense - Route 10 - Nosepass (! EV) x 2 (Brace) x 2 (Pokerus) x 5 (horde) = +20 EVs
Special Attack - Frost Cavern - Vanillite (1 EV) x 2 (Brace) x 2 (Pokerus) x 5 (horde) = +20 EVs
Special Defense - Route 7 - Hoppip (1 EV) x 2 (Brace) x 2 (Pokerus) x 5 (horde) = +20 EVs
Speed - Route 8 - Wingull (1 EV) x 2 (Brace) x 2 (Pokerus) x 5 (horde) = +20 EVs
This means it'll take 8 Horde Battles per stat after the vitamins to reach 252 in each of the 2 main stats (you can't go over 252) equaling 16 battles altgother after consuming 20 vitamins. For the third state, simply drink a matching vitamin to get the +4, hitting the cap of 510 for all practical purposes (technically, you'll be at 508 but other +2 you could get would not do anything as it takes 4 EVs to equal 1 stat point).
There are special items you can get with Battle Points from the Battle Maison (in Kiloude City) that give +4 EVs to a particular stat instead of wearing the Macho Brace:
Power Weight - Health
Power Bracer - Attack
Power Bend - Defense
Power Lens - Special Attack
Power Band - Special Defense
Power Anklet - Speed
Adjusting the same horde areas for the Power Items:
HP - Route 5 - Gulpin (1 EV) + 4 (Power Item) x 2 (Pokerus) x 5 (horde) = +50 EVs
Attack - Route 14 - Bellsprout (1 EV)+ 4 (Power Item) x 2 (Pokerus) x 5 (horde) = +50 EVs
Defense - Route 10 - Nosepass (! EV)+ 4 (Power Item) x 2 (Pokerus) x 5 (horde) = +50 EVs
Special Attack - Frost Cavern - Vanillite (1 EV) + 4 (Power Item) x 2 (Pokerus) x 5 (horde) = +50 EVs
Special Defense - Route 7 - Hoppip (1 EV)+ 4 (Power Item) x 2 (Pokerus) x 5 (horde) = +50 EVs
Speed - Route 8 - Wingull (1 EV)+ 4 (Power Item) x 2 (Pokerus) x 5 (horde) = +50 EVs
This means it'll only take 4 Horde Battles to max out a stat's EVs after Vitamins or 6 Horde Battles total without. This is the best way though it does require first beating the Elite Four and acquiring Battle Points (16 each).
Natures
The next piece of the puzzle is making sure you'll get the right nature for your pokemon. You can which one you have by IDing your pokemon. The nature influences which stat gets a 10% bonus and which stat loses 10%, they are:
Lonely - Attack > Defense
Brave - Attack > Speed
Adamant - Attack > Special Attack
Naughty - Attack > Special Defense
Bold - Defense > Attack
Relaxed - Defense > Speed
Impish - Defense > Special Attack
Lax - Defense > Special Defense
Timid - Speed > Attack
Hasty - Speed > Defense
Jolly - Speed > Special Attack
Naive - Speed > Special Defense
Modest - Special Attack > Attack
Mild - Special Attack > Defense
Quiet - Special Attack > Speed
Rash - Special Attack > Special Defense
Calm - Special Defense > Attack
Gentle - Special Defense > Defense
Sassy - Special Defense > Speed
Careful - Special Defense > Special Attack
Hardy, Docile, Serious, Bashful, and Quirky give no bonus to any stat, nor do they give a penalty to any stat.
As an example, for an offensive pokemon, a Speed nature is usually desired with Timid and Jolly being used for Special Attackers and regular Attackers respectively. Naive and Hasty are better used for mixed attacker that utilize both offensive stats.
When breeding, you can ensure there's a 50% chance of the offspring having a certain nature by having a parent with the desired nature hold an Everstone.
In order to catch a pokemon with the correct nature, using a Pokemon with the Synchronise ability gives a huge chance of the pokemon you encounter having the same nature as the synchoniser leading off. Abra and Ralts are good choices.
Effective Breeding
Now that we know about IVs, EVs, and Natures, let's put it all together!
Step 1 - Using a Synchroniser (Usually Abra, Munna, or Ralts), with the nature you want (encounter rate of the wild Pokemon matching the Synchroniser's nature is 50%), encounter a Female pokemon with the Nature you want from the Friend Safari (Female Pokemon pass down their species). In this case we'll choose a Kirlia (Ralts' evolved form) with the Timid nature:
I would recommend starting off by finding a friend who has a Kirlia Friend Safari in X/Y. You can accomplish this easily via the many, many Pokemon forums (serebii, 4 chan's /vp/ page, etc).
Remember: the important thing about the safari is that any pokemon found in them will automatically have 2 of their 6 IVs set perfectly to 31.
Step 2 - Catch any compatible Male pokemon, check serebii in the button below for a list of all the egg groups. In general, the same pokemon or Ditto will always work but sometimes you may want the "Egg Moves" of a certain pokemon and though either gender can pass down these "Egg Moves" (again, information available in the button below), you may want to focus, at first, on the male having these moves. In this case, we'll use a Kirlia again.
Step 3 - Head to Kiloude City and check which stats are 31 by talking to the guy in the pokemon center in purple. You can Mark them in the PC via the Mark Pokemon option after selecting the pokemon or just take a note somewhere about which stats are perfect.
Step 4 - Give the Timid mother the Everstone and the Father the Destiny Knot and head to the Day Care, desposit both, then begin Masuda's Bike Simulator (riding back and forth), scoop up the eggs, hatch, then check with the NPC in Kiloude, mark down the stats, and keep repeating, replacing the parents with offspring that have more stats at 31 IV (making sure the Timid mother has the Everstone and the father holding the Destiny Knot.
Step 5 - Now that you have a Timid Ralts with 31 IVs in HP, Defense, Special Attack, Special Defense, and Speed (Attack stat doesn't matter in thise example though some people like any non-Attacker to have 0 IV in Attack due to the Foul Play attack), have it drink 10 Carbos (100 Speed EVs) and 10 Calcium (100 Special Attack EVs).
Next, infect it with Pokerus and, holding the Power Lens, go out to Frost Cavern and have Venusaur use Sweet Scent and Petal Blizzard to draw out, and KO, 5 Vanillite at a time 4 times total.
Now that your Special Attack is maxed, replace the Power Lens with the Power Anklet and go to Route 8 and defeat 4 Wingull hordes with Venusaur to top off Ralts' Speed EVs.
Finally, have Ralts drink an HP Up to get that final +4 EVs into HP.
Step 6 - Make sure Ralts/Kirlia/Gardevoir has the moves you want (Moonblast, Psyshock/Psychic, Calm Mind, and Focus Blast as an example), level it to at least 50 for Nintendo's Competitve Play, equip a useful item to it (Gardevoirite?) and have fun!