IV Breeding

Theoretically, you IV breed then only you EV train.. But the reason it's put after EV training is because it's less important compared to EV train or nature.. Slightly unlike EV training.. If EV training is all about effort.. Then I would say IV breeding is all about luck..

What's IV breeding?
"IV" stands for Individual Values.. Just like us, some of us are born with a better creativity, athletic or smart while some are less fortunate.. Pokemons have these IV ranges from 0 to 31 each stats.. It acts like a ratio, so of course 31 is the best.. A Pokemon with 31 IVs in all its 6 stats is called flawless pokemon..

Now let's talk about "luck".. 3 IVs are RANDOMLY taken from any parents.. While the other 3 IVs are total random.. However, there's Power Items which can fix one of  the parent's IV for his/her child.. So assuming one of the parents have a max IV, you can easily pass down to the child, but don't forget about nature.. Another parent will have to get his/her nature pass down to his/her child with Everstone.. What I am trying to imply is, getting a correct nature with one 31 IV is pretty simple.. You can probably get it less than an hour.. But if you are aiming two 31 IVs with correct stat, it should spent you an hour.. 3 max IV with correct nature will takes you hours, or maybe days if you are aiming for really good IV.. I just want to let you know this before you start.. :)

Why IV Breed?
Probably if you want to try wifi battle.. Otherwise it doesn't play any important role in game unless you are crazy about Battle Subway.. This is my opinion if you ask how "important" is IV in wifi battle.. Let's say both you and your opponent started with a Gengar with Timid nature.. And both of them have 252 EVs in Spd and Sp.Atk stats, which isn't surprising.. In this case, whoever has the first hit has a high chance killing opposing first with Shadow Ball.. So the question now is who goes first? The answer will be your IV.. Even if it's just a difference of 30 and 31.. It will decides who lands the finishing blow..

How to Know the IVs of Each Pokemons?
Let me say this first, you can only check a Pokemon's IVs if you know its EVs.. If it's a newborn/new-caught Poke, then it has 0 EV.. But if it's the Poke which you used to battle randomly in game, you can't check its IV without hacking the game..

There's few ways... You can get a rough reading from a boy with blue hair in Battle Subway.. First he will tell you the overall IV of your Poke.. The best would be "Outstanding", with nearly all stat above 28 IVs, followed by "Relatively superior".. Then he will talk about its highest IV (he will mentioned all if there's more than one of the same value) and the rough value of it.. The best would be "It can't be better", means that Poke has 31 IVs on that particular stat.. Followed by "It's fantastic", which should be around 2x~30..

The second way is the Rare Candies method.. You will need at least 30 of it.. The reason we use Rare Candies is because there's no EV invest.. So you can Rare Candy a Poke till lvl 30 + to know its stat better.. Once you have a "clearer" stat, go to the net and check for IV calculator.. Type the nature, stat etc. into it and it will tell you all of its value.. The more Rare Candies you use, the more accurate it is.. 50 should get you an accurate result..

The third way will be wireless/wifi battle with a friend.. You will, probably, want to lose on purpose in this case.. Set a battle fixed at lvl 50/100 with your friend.. Then during your turn, check and write down all of your 6 Pokemons' stat.. After the battle, go to the net and check with the IV calculator..

The third way will be PWT, you can enter the Unova tournament.. Save before you participate.. They will default your Pokemon lvl to 50.. Then from there, note down all your 3 or 4 Pokemons.. Then use IV calculator to check their exact IV.. After you are done, just reset your game.. *Credit goes to Gayr*

What you need for IV Breeding
All Power Items, or at least the important ones.. These Power Items will fixed one of the parents' stat.. Means you can have easily 2 stats fixed, assuming that the parents have good/max IV..

Everstone, I bet without effort you will have one.. And you should know it's pretty useful for breeding as well.. This item fix one of the parents' nature to pass down to his/her child..

Last but not least, lots of Dittos.. I'm not sure if you are willing to spend time on this, but I do think it's helpful.. Try to get at least a box of Dittos.. You should be able to get all the important natures such as Adamant, Timid, Modest etc.. Meanwhile, you should also get some with max IV in their stat.. Release all the "useless" ones, keep each of good natures and max IV of each stat.. You might want to name them and write down in your notepad so you can recognize them..

How to IV Breed?
Just like your usual breeding, attach Everstone to the Ditto with the nature you want and breed with the Poke you want..

Ditto with Everstone (Nature) x Poke = Child 1 (Nature)

Once you get the nature correct, breed it with another Ditto with the max IV you want WITH the correct power item attached to it..

Ditto with Power Item 1 (No.1 Max IV) x Child 1 with Everstone (Nature) = Child 2 (No.1 Max IV & Nature)

Once you have another child with the max IV and the correct nature, attach the previous power item on it.. And get another Ditto with another max IV you want, of course attach the power item that fixed it.. Breed both of them..

Ditto with Power Item 2 (No.2 Max IV) x Child 2 with Everstone (No.1 Max IV & Nature) = Child 3 (No.1 & No.2 Max IV & Nature + Time)

From here, you are close to getting what you want, all you have to do is wait till a child with two max IV.. To improve your chance/poke even greater.. The result will be based on your luck and requirement.. Keep switching the parents with the child if the child's IV is better, even if both of them have the same max IV, because this way, you no longer need to attach that particular power item as the chances of getting it fixed is slightly higher.. If you are lucky enough, you might even get extra max IV out of no where.. Keep doing this till you get your ideal Ability, Nature, two max IV you wanted and the guy in Battle Subway says it's overall IV is "superior" or better still "Outstanding"..

Dream World Ability
Female parents have their own role as well, they increase the chance of the child getting same ability with them.. But obviously passing down DW ability is like 10 times harder.. Simple, because both Parents must not be Ditto to pass down the ability.. Second, passing down DW ability is not even 50%.. Third, DW ability can only pass down by the FEMALE Poke.. But don't worry, Ditto is not useless even if the first rule apply..

Ditto with Everstone (Nature) x DW FEMALE Poke = MALE Poke (Nature)  

MALE Poke with Everstone (Nature) x DW FEMALE Poke = DW FEMALE (Nature)

Ditto with Power Item 1 (No.1 Max IV) x DW FEMALE with Everstone (Nature) = MALE Poke (No.1 Max IV & Nature) 

MALE Poke with Power Item 1 (No.1 Max IV & Nature) x  DW FEMALE with Everstone (Nature) = DW FEMALE (No.1 Max IV & Nature) 

Ditto with Power Item 2 (No.2 Max IV) x DW FEMALE with Everstone (No.1 Max IV & Nature) = MALE Poke (No.1&2 Max IV )

MALE Poke with Power Item 2 (No.1&2 Max IV ) x DW FEMALE with Everstone (No.1 Max IV & Nature) = ~

Moves
Moves can only be passed down by the MALE parent, kinda reverse of DW.. However it should be faster/easier because passing down move(s) is 100%.. Not only that, you can breed it with Ditto just to pass down its move.. As long as you haven't take out the male the parent, it will keep on passing his move to the child even if it's erased by the breeder (of course you don't know whether it's deleted or not). But be aware that the moment you took the male out, there's a high chance that his move will be erase.. Even if you put him back, he won't be able to pass down the old moves to his child.. So if you doesn't want that to happen, delete one or two moves to that the Breeder won't erase his move randomly..