>The Masuda method (Japanese: 国際結婚 international marriage), also known as Masuda's method, is a fan-made term which describes a way to obtain Shiny Pokémon more easily from Generation IV onwards. While the standard encounter rate for a Shiny Pokémon (either in the wild or by breeding) is 1/8192, the Masuda method multiplies this rate by 5 (to 5/8192 or about 1/1638) in Generation IV and by 6 (to 3/4096 or about 1/1365) in Generation V. It occurs whenever Pokémon of differing real-world geographical origin are bred.
The method is named after Game Freak director Junichi Masuda, who programmed it into Pokémon Diamond and Pearl. He documented the method in his blog, where he mentioned a way that "rare colored Pokémon's Egg can be found little easier." The mechanics behind the method were discovered by Smogon.
The Masuda's Method is very easy to do and increases your chances by a lot (1/1638 or 1/1365). Simply obtain a Pokémon from a different language speaking country than your own and put it in the daycare with your own Pokémon as usual. Eggs hatched will have a better chance of being shiny. I would reccommend this method the most, since it requires less effort than the others and you don't need to worry about breaking a chain (see below).
Some other ways of obtaining shinies are Chain Fishing, Dexnav Chaining and the Pokerader.
All of these involve chaining. Chaining is when you repeatedly encounter the same species over and over again, increasing your shiny chances.
Chain fishing is when you fish in the same spot over and over again. This increases your shiny chances, but moving spots or failing to reel in a Pokémon breaks your chain. To make sure you always get a bite, you should have a Pokemon with Suction Cups or Sticky Hold in your party. In this method, its okay to encounter Pokemon of different species. I personally find it a bit difficult, but many people find it easy enough. The problem with this method is that the kinds of shinies you can get are more limited to water Pokémon.
Dexnav chaining is when you search for a Pokémon on the dexnav and encounter the same Pokémon over and over (chaining the Pokémon). Once you get a chain of 40 (very difficult), your chances get up to 0.5 which is a huge improvement. If you encounter a Pokémon of another species of the one you're chaining or fail to encounter the Pokémon (scaring it away, waiting too long, etc.) your chain will break. This method is rather difficult, especially when chaining in water, sand, cave, Mt. Pyre, etc. because the Pokémon can move locations.
The Pokerader is possibly the most difficult of all methods. To do it, you have to step into a large area of grass (if the area is too small you wont be able to chain successfully) and use it. Different music will play and patches of grass will shake. You have to step into the closest patch of grass, except you cannot step into patches that are too close, around the sides, shaking next to another patch and more, or your chain will most likely break (I do not know all the ways a chain could break, but there might be some online guides). You also cannot hatch eggs or encounter Pokémon of a different species than the one you are chaining. Sometimes the chain may just end for no reason. You will know when your chain breaks when the pokerader music ends and the regular route music starts. When you see a patch of grass sparkling, this means it has a shiny Pokémon. I don't recommend this method and it is extremely hard to get anywhere close to a shiny.