Instructions
Start Pokémon Sapphire and choose to begin a new game on the main menu. If there is already a save file present on the game cartridge, it will be overwritten when you save a new game. Choose your character's gender and name and start the game.
Leave your in-game house after speaking to your character's mother and viewing a short cut scene. Enter the house directly across and and speak to your rival. Leave the house and head north until you enter Route 101.
Approach the bag of Professor Birch who is currently being attacked by a wild Pokémon. Inside the bag are three Pokémon. Before you choose one, save your game.
Pick whichever Pokémon you like and use it to defeat the Pokémon that is attacking the Professor. Afterwards, the Professor will let you keep the Pokémon you picked from his bag.
Open the Pokédex and check to see if your Pokémon is shiny by looking at the coloring on the number next to its name. If it is gold, it is shiny. If not, perform a soft reset on the system by holding down the "A," "B," "Start" and "Select" buttons.
Reload your save file and pick a Pokémon again. Continue resetting and reloading until you get a shiny Pokémon.