As has been said, 1:8192 chance of seeing a Shiny. That doesn't mean that it never happens early, though. I found my Golden Shellder the first time I used Super Rod. Don't get your hopes up; I have been soft-resetting for Shiny starters for four days now.
To soft-reset for a Shiny Starter, save in front of the Pokeball containing your preferred Pokemon in Prof. Oak's lab. Take the Pokemon, wait for Gary to get his, then open your menu to look at its primary status page (where the picture is). If it isn't Shiny, hit A+B+Start+Select (all at the same time) to soft-reset and try again.
You can use the soft-reset method anywhere someone gives you a Pokemon, or you can see a Pokemon's sprite before battle (Legendary Birds, etc.)...
Most people see at least one Shiny in the course of the game... chances in the wild are the same, but you never know when your Shiny will come. So be prepared!! Have lots of Balls on hand, or use the Gameshark to max your Balls case inventory. That way, you have 99 of every single kind of Pokeball. Luxury Balls are nice; they make the Pokemon like you more.
Whatever you do, don't use any Poison, Confusing, Leeching, Burning, Wrapping, Constricting, Nightmare, or Cursing moves!!!!!!!!
And God have pity on you if you see a Shiny in the Safari Zone, LoL!