Instructions
Make sure you have at least five Poke Balls before venturing into tall grass to catch wild Pokemon. When searching for shiny Pokemon, you don't want to get caught without the right supplies to catch them.
Walk through patches of tall grass for an extended period of time. You have a 1-in-8,192 chance of running into a shiny in the wild in Ruby.
Ride your bicycle to increase the amount of Pokemon you run into while in the tall grass.
Place a Pokemon with the natural ability "Illuminate" in the front of your party (e.g., Staryu, Starmie) to attract wild Pokemon. This will increase the number of encounters you have with Pokemon in tall grass and give you a better chance at finding a shiny.