In Generation II, Shininess is determined by the IVs of a Pokémon. If a Pokémon's Speed, Defense, and Special IVs are all 10, and its Attack IV is 2, 3, 6, 7, 10, 11, 14 or 15, it will be Shiny. ...
...In a wild encounter, the probability of a Pokémon's IVs lining up in any of the above manners is 1/8192; breeding has different odds due to parents passing on IVs to their offspring. For example, if one breeds a Shiny Pokémon properly, the offspring may have as high as a 1/64 chance of being Shiny, depending on the species of Pokémon.