In order to get a special stage you have to catch three pokemon in one place.

For example: If you catch Pikachu, Pidgey, and another Pidgey in Viridian forest, without getting a "game over", or switching to somewhere then back again, a hole will appear saying "Go To BONUS". Go in and you will be in the stage.

The Red field Bonus Stage is Diglett's Cave and the Blue field Bonus Stage is Meowth's House.