Do not "try" and find a shiny in Gen 3, you will go crazy. Just play the game through and hope you find one along the way. Or you could soft reset for a starter/legendary, but you probably will go crazy doing that also. :s
"...Nintendo's work environment is a playground. Sony and Microsoft force you into cubicles of terror where you program til you die." - RahzarX
I restarted my Ruby game 4 times and found a shiny each time. Zigzagoon was the first pokemon I ran into after getting my starter and it was shiny. Second run, I found shiny Spoink on the way down from the mountain. Third playthrough gave me shiny Tentacool while surfing from the town by the daycare. And last time another shiny Zigzagoon showed up.
Was able to send the last two to gen 4 cause Diamond was out by then.