It's all luck...
Hey!
I agree with everyone. It is completely a matter of luck. I've played through Crystal several times. I've concluded the following;
A.) The greatest CHANCE you have of getting a shiny is that Odd Egg that is given to you by the Daycare Couple. however, I am not sure if the Odd Egg is available in G/S, so...
B.) Be prepared for a LOT of searching if you are "hunting" shiny's
C.) About the stats;
I will try to get more precise data soon on Shiny's and their stat's. But from what I've seen (and read), Shiny Pokemon have above average DV's. Contrary to Popular Belief, however, they aren't complete DV's (a full 15 in GSC)
D.) Luck; only once did I ever encounter a shiny pokemon randomly walking around... It was a shiny Graveler (yeah, i know... wish it was a Lugia ;)
in a cave...
*Just remembered
I did encounter a shiny Pikachu once... in that area near Pallet Town (Route 1?)
Riad