Pokemon Breeding is a patience sport like fishing. Once you have the know-how and the right equipment it's really just a big endurance test, and that's why a lot of people are turned off by it. Personally I like it. It's very rewarding to finally see the final product, and I earn every victory. With all the Pokesavers running around, Legitimate Breeders are becoming fewer and fewer. Which is why I've decided to pass on my knowledge to the youth!
The first things you'll need are some synchronizers. This is useful when looking for a Ditto of a specific nature, as well as potential parents. I've found that the best way is to purchase some Abras from Celadon's Game Corner in Fire Red and Leaf Green. You'll need to buy enough coins for at least five Abras, then save in front of the appropriate coin exchanger. Proceed to buy as many Synchronizers as you need, soft resetting when you've received a bad batch. Then it's simply a matter of migrating the synchronizers to your version of choice. Alternatively you can simply breed them, or use the Pokeradar.
Next you'll need some good Dittos. Having a ready supply of Dittos is a must for any competent breeder. However, there's no need to be extravagant; a properly natured Ditto with 31 in any one of the desired states should do for now.
The easiest way to go about doing this is to use the Pokeradar in Pokemon Diamond/Pearl. Unfortunately this is a lot harder to do in Platinum because Ditto is found only in the Pokegarden. Bring a lot of Repeat Balls and use a Synchronizer equipped with a Smoke Ball as your lead. You'll need to remove Teleport from any applicable Synchronizers, as the best strategy is to let Ditto transform into your Synchronizer and then go from there.
When all is said and done you should have a hoard of Dittos waiting in your PC when your streak ends. Use the Dittos characteristic to determine which ones are worth checking and which ones need to be tossed. Repeat as necessary. Once you've obtained enough Dittos, it's time to get breeding. You'll also want some everstones, along with the power items if you're breeding in Heart Gold/Soul Silver. Don't worry though, this only has to be done once and you're set for life.
-Two compatible Pokemon left in the daycare will produce an egg.
-Males pass on their egg moves.
-Females/Ditto equipped with Everstones pass on their nature.
-Any gender can pass on any IV when equipped with the appropriate Power Item.
-When both parents know the same attack, that attack is passed on to the children.
-TM moves will pass just like Egg Moves.
-There's no way to improve the odds of one ability passing over the other.
-The egg's nature/IVs/ability is determined when you receive it.
-Pokemon with Flame Body/Magma Armor reduce the amount of steps it takes to hatch eggs in the same party by half.
-The parents collectively pass on two to three of their IVs when breeding
-Having two parents with the same IV greatly improves its chance of passing.
-HP has a lower chance of passing than the other stats
Breeding in Practice
Now you'll want to put a Pokemon with Flame Body/Magma Armor in your lead spot, and then deposit whatever else you have in your PC. For the sake of this guide we'll assume I'm breeding an Adamant Garchomp. First I take my Bashful Gible (Any Gible, it doesn't matter.) and leave it in the daycare along with my Adamant Ditto with 31 IVs in Speed. I equip the Ditto with Everstone to pass on its nature, and leave the Gible unequipped since it doesn't have an IV worth passing at this point.
Once I have a Female Adamant Gible with 31 in speed, it's time to remove the parents from the day care. I put the Ditto aside and release the Gible; they've served their purpose and won't be used again for this breeding project. My next step is to put the female Adamant Gible in the Day Care along with a compatible Male Pokemon with 31 IVs in Attack equipped with a Power Bracer. The next goal that needs to be worked towards is having both parents with 31 IVs in Attack and Speed.
Once I've achieved this there isn't much more to do other than replacing the parents whenever a Pokemon with higher IVs comes along. Aiming for both parents having 31 IVs in three stats (Attack, Defense, and Speed in this case) is ideal, and using the Power Items will go a long way in achieving this goal. At this point breeding becomes a simple test of patience.
The End Result
? Adamant - 30/31/31/26/30/31
There are a few different methods to checking IVs. The best (and most popular) of them is through an IV Battle. An IV battle isn't really a battle at all, of course. Two Trainers get on wifi and start a battle with their Pokemons' levels boosted to 100. This allows them to see their Pokemons' IVs with a perfect level of accuracy, using an IV calculator.
Alternatively you can use Pokemon Battle Revolution to boost them to level 50, but this is less accurate. You can also save your game, and then use Rare Candies to boost your Pokemon to level 100. This however is extremely time consuming and impractical.
Tips & Tricks
-When breeding, it's inefficient to hatch eggs five at a time. Whenever you hatch an egg, Deposit/Release it and then ask the Day Care man for another one.
-Breeding requires very little attention, so I suggest breeding while watching TV or a movie. Setting your button mode to L=A even allows you to do it with one hand. This makes things a lot easier as breeding can be rather time consuming.
-Having two DSs and two 4th gen Pokemon games available makes things considerably easier, as you no longer have to have someone help you check your IVs.
-When in the later stages of breeding, when both parents have 31 in all of your desired stats, it might be a good idea to use the power item on a different stat, since having both parents with the same IV increases the likelihood of it passing already.
-A man in the Celadon Game Corner Prize Room can quickly tell you what Hidden Power your Pokemon has.