I want a shiny snivy!
In Generation V, it (the probability of obtaining a shiny via the Masuda method) is boosted even further from 1 in 8,192 to 1 in 1,365.3.
So these are your chances of getting a shiny via the Masuda method.
If, however, you're using the Masuda Method to breed, (the shiny charm) reduces it from 1 in 1,365.3 down to 1 in 1024.
This is your chance of a shiny by using the Masuda method while having obtained the Shiny Charm for catching every Pokemon in the National Pokedex (bar event legendaries).
Serebii on shinies
The shiny charm increases the chance of finding them in the wild. I don't think there are any other ways to increase the chance of getting a shiny Pokemon through breeding other than the masuda method.