Here is how to get a shiny pokemon in Pokemon Crystal Version: Well, the way that probably everyone knows, go to the lake of rage and find the red gyarados in the middle.
But for a less obvious way: On route 34 (or whatever route comes right before Goldenrod) you should see a building with a pen. That's the daycare, make sure you have an empty slot in your party. Talk to the old guy in there, but save before you do. He will give you the Odd Egg, it will hatch into 1 of 7 pokemon: Tyrouge, Magby, Elekid, Pichu, Cleffa, Igglybuff, or Smoochum. That's why you save before you get the egg, and DO NOT SAVE AT ANY OTHER TIME UNTIL THE EGG HATCHES, OTHERWISE IT'LL BE THE SAME POKEMON EVERY TIME. I read on some website that the egg has a 14% chance of hatching a shiny pokemon, so that's another reason you should save before you get the egg and no other time at all (until it hatches, if you like it, save, if you don't, try again) It works, trust me, my first egg was a cleffa, so I turned it down, because I wanted a magby. My second egg: Shiny Magby. Try it out, it might take a few tries though. The person I got it from said after 15 eggs, he got what he wanted, a Shiny Elekid.
Note: The baby starts with Dizzy Punch no matter what it hatches into out of those 7.
I hope this helped! ; )