Instructions
Travel onto any patch of grass, into any cave or onto any body of water. Generally, any location where you can be attacked by a wild Pokemon is a good location to search for shiny Pokemon.
Place a Pokemon that knows the move "Sweet Scent" in your party. Select the Pokemon from the main menu and use "Sweet Scent." This will cause you to be automatically attacked by a wild Pokemon, reducing the time spent walking around.
Select "Run Away" from the battle menu if the Pokemon is not a shiny Pokemon or simply defeat it. If the Pokemon is a shiny Pokemon, a little twinkling star will appear at the beginning of the battle.
Attack the Pokemon to lower its health, but do not defeat it. Once its health is in the red, use a Pokeball to capture it.