This will work on Diamond, Pearl and Platinum.
How to do it:
One parent has to be international, from another country, and the other parent from your own game or different nationality to the other Pokemon.
International means foreign, like Japanese, Spanish, French, German, and so on, assuming whoever's watching this video's game is English. English is both the Americas and the UK.
If you are using a US game, catch a Pokemon from your own game and breed it with say a Japanese Pokemon, and vice versa.
You can apparently use Pokemon not from the GTS, they just have to be international. So if you have a friend with, say, a Japanese Platinum, get them to do you a favor and trade you a Japanese Pokemon of your choice, like a Japanese Ditto to breed with any of your own English Pokemon.
WARNING: Meister the Hiker on Route 226 trades you a German Magikarp for a normal Finneon. HIS WILL NOT WORK BECAUSE THE CODE FOR THE MAGIKARP IS GENERATED ON YOUR GAME.
The reason this Masuda Method was put into the game was to encourage trading WITH REAL PEOPLE FROM AROUND THE WORLD.
You HAVE to use a foreign Pokemon you get in a real-life trade, period.
Now I want my own Japanese Diamond. =\
How it works:
The game checks to see if the breeding parents have different nationalities from one another. If they do (I.E. English/Japanese, Japanese/German), it goes through the shiny frames 4 times.
Therefore, the chances of obtaining a shiny go from 1/8192 to the much better 1/2048.
It will still be tricky to hatch a shiny, but it will still be easier.
Hopefully either will work.
Junichi Masuda is practically head director of Game Freak, which has been working on Pokemon games since the very beginning. I don't think he'd lie.
Copy pasta from Masuda's blog:
'Welcome! This is the Global Trade
Station, or GTS for short.'
GTS starts with above message by the lady
at the counter.
I have a confident that the player will sure
to trade their Pokemon at least once with this GTS system.
However, I wondered how we could make the trade
number of times...
Not only domestic, but overseas trading,
especially the people you have never met.
This was the big theme of creating GTS in
Pokemon Diamond and Pearl.
I believe high game playability means,
to make the game fun playing many times repeartedly.
Same as this GTS.
So we considered the following contents.
=some Pokemon's Pokedex descriptions are written in foreign language,
=automatic mail translation,
=the location of the opponent you traded is pointed on the globe,
=country/city name is indicated when you set the cursor on the point,
=rare colored Pokemon's Egg can be found little easier,
=Pokemon traded with different country have better growth
than the one normally traded,
Ideas like above are incorporated in the game.
It requires a very large effort to make the player
to play one certain thing.
Once the player lose the interest to the "Play",
they will stop playing very easily.
To make the player not to get bored
(which means 'to make the player addictive'),
it is important to set the variety of enjoyment entangled.
Even it's a small,
if the idea's theme is set to the right course,
it is substantial to embrace to the game.
Putting together the small pieces of fun elements,
those make the game more luxurious.
Like this GTS,
It is very important to enunciate the theme
loud and crystal clear.
rare colored Pokemon's Egg can be found little easier,
This sort of set the community on fire.... quietly. It was oft overlooked, but they have finally cracked what this genius' code is:
Breeding with a foreign Pokemon, like, say, FROM THE GTS, gives you 1 in 2048 odds of hatching a shiny as opposed to the real tough normal 1 in 8192 odds.
Let's get hatchin'!!
Thanks to MetalMario of PokeCommunity for bringing this to my attention, even though I along with someone else (if you're still out there, speak up!) reinserted Masuda's words of wisdom back into the community.
And thanks to shinyhunter for clearing the confusion :)