Thanks to Gen 6's new breeding mechanics, obtaining perfect Pokemon is now possible and doesn't even require a huge amount of work. As always, attaining total perfection is optional and is not really necessary in most cases, but it can be done and some people are going to want to do it.
First, you have some setup to do before you start breeding:
You must have beaten the Elite 4. It's not even worth breeding until you have done so, as Friend Safari simplifies breeding insanely much.
Find someone with Dittos in their Friend Safari and catch a lot of them. The goal here is to get one with every useful nature. They do not need to have their hidden ability.
Once you have your dittos, take them to the IV checker in the Kiloude City Pokemon center. Each of them will have (at least) 2 perfect IVs, and he'll tell you what they are by saying that they "can't be better". Nickname your dittos based on what perfect IVs they have. For example, you could call one "AtkDef" if Attack and Defense were their perfect IVs.
You should also obtain all of the power items (Power Band, Power Anklet, etc) from the Battle Maison, the Everstone from an NPC in Geosenge Town, and the Destiny Knot from an NPC in Cyllage City
You are now ready to breed obscenely powerful Pokemon:
Get the Pokemon you wish to use. If you want its hidden ability, you'll need to get one from the Friend Safari. Breed it with a Ditto of the right nature that holds the everstone. This guarantees the baby will have the right nature, but you are not guaranteed to get the hidden ability if you're breeding for it, so make sure you retain the hidden ability if you're after it. This also applies to all further steps when dealing with hidden abilities.
Next, breed this Pokemon with a Ditto that has a perfect IV that you wish to have, and give it the appropriate power item. Move the Everstone to the Pokemon you just bred. The baby will now have a perfect value for that IV, as well as the right nature.
Breed this new baby with a different ditto who has two different perfect IVs, holding a power item for one of its perfect IVs. Your baby should continue to hold the everstone. The goal here is to get a baby with 2 perfect IVs, which is about a 1 in 3 chance. Take all of your babies to the Kiloude city IV checker until one has 2 perfect IVs.
Breed this new baby with yet another ditto who has two different perfect IVs. Between them, your Pokemon should now have 4 perfect IVs, so give the ditto the item Destiny Knot. Your baby continues to hold the Everstone. At this point, your Pokemon have a good chance of hatching with 3 perfect IVs.
Once you get one with 3 perfect IVs, again make that baby the new parent and have it hold the everstone, and get another ditto with 2 different perfect IVs and give it Destiny Knot. Do the same when you get your first 4 perfect IV baby. The eventual goal here is to breed a baby of each gender with 5 perfect IVs and make them your parents.
When you have both parents having 5 perfect IVs holding Everstone and the Destiny Knot, you have about a 1 in 200 chance that a hatched baby will have completely perfect IVs. Good luck.
Don't throw away male babies with 5 perfect IVs. These can be used in place of dittos to breed with other Pokemon in their egg groups, and you can use Destiny Knot right from the start to speed up this process dramatically.
Disclaimer:
Getting 5 perfect IVs, and certainly all 6, is very rarely necessary. The difference between IV 25 and IV 31 is very small for all stats except Speed. In fact, getting all 6 IVs perfect will lock you into a specific hidden power, which may not be the one you want. It's up to you to decide how far you will go with your breeding process.
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