I believe the fastest way is still Chain Fishing. Put a Pokemon with either Sticky Hold or Suction Cups in the lead of your party to ensure you get a bite on each cast of the Rod of your choice. Cast repeatedly, reeling in the Pokemon each time. You can faint, catch, or run from the Pokemon, that part is unimportant. What IS important is that you not miss a cast, and that you DO NOT move from the spot you are standing in. Reports are that, on average, you will encounter a Shiny around the 25th cast. However, you have little control, beyond the type of Rod you use, of what Pokemon it will be when it finally does pop. You will also have no control over it's IVs, Nature, Ability, or the presence of any Egg Moves with this method.
The tried-and-true method of obtaining Shinies, with the greatest control over the resulting Pokemon, is the Masuda breeding method. The easiest way to perform the Masuda Method is to obtain a Ditto originating from a different language, and breed it with the desired Pokemon. This dramatically raises the odds of the Pokemon hatching from the eggs to be a Shiny, and is a 100% compatible with IV, Nature, Ability, and Egg Move breeding if you are so inclined for Competitive purposes. I have used this method to breed a Shiny 4 IV Protean Froakie, as well as a Shiny 5 IV Speed Boost Torchic. I am currently working on getting a Shiny 5 IV Giga Drain Bulbasaur, it is proving elusive. I have in fact bred a number of Shiny Bulbasaurs, but the IVs have been in the wrong places.
As a little aside, there is also a built in feature of the game that will increase your odds of encountering Shiny Pokemon overall, stacking with other methods of increasing Shiny odds. It is called the Shiny Charm. It is a Key Item you receive when you have captured all of the non-Mythical Pokemon, adding their information to the Pokedex. Show the Professor your work, and he will give you the Shiny Charm.
