I think Fiery`Arcanine is talking about the verisons Gold, Silver, and Crystal. In the Generation II Games, wild Pokemon would be shiny if their Individual Values [IVs] were better than average. That was the last game that the Pokemon's shininess was determined by Individual Values. Ruby, Sapphire, FireRed, LeafGreen, and Emerald all had shiny Pokemon randomly generated.
Now, there is a method to increase the chances up to about a 1/200 chance, I believe. It is called PokeRadar chaining, in which the device of the PokeRadar is used to make a chain of the same species of Pokemon. For example if you are chaining Bidoof, it would require you to encounter so many Bidoofs in a row. If you ran into a Starly, your chain would be broken and you have to start all over. You can read about this chaining method in the Diamond and Pearl FAQ.
I think I've strayed the topic at hand a little. In short, you cannot make a Pokemon shiny. You have to encounter it as a shiny Pokemon. If you encountered, lets say your Bidoof, as a normal colored Pokemon, there is no way to turn it into a shiny Pokemon. If you want a shiny legendary, you should keep soft-resetting for one.
Latias and those runaway Pokemon are hard to get, since those Pokemon's shininess is determined at the start of the game. Egg Pokemon's shininess is determined the first time you receive the egg.
In case you're wondering...
Each time you encounter a Pokemon, it has a 1/8192 chance of being shiny. Trainers can go through their whole gaming career without seeing a shiny Pokemon, because it's that rare.