How do you raise the chances of getting shiny Pokemon?

Answer:It depends on very, VERY good luck to get a shiny Pokemon. The odds of finding one in the wild are 1 to 8192 battles...and if you're lucky enough to find one and try to breed it to get an egg, it won't produce another shiny.

The only known way of raising your chances of getting one are encountering more Pokemon in the wild or using a GameShark/Codebreaker code.

They can produce a shiny if bred, but they wont always. The odds are much better if you catch and breed. It goes from 1 in 8192 to something like 1 in 64. Also, If an egg is bred from two Pokémon which were created in games of a different language from one another (either by capture or by breeding), the resulting egg is four times as likely to be shiny when it is generated. (bulbepedia)