Instructions
Capture Mewtwo at the end of Cerulean Cave after defeating the Elite Four in either "Pokémon Red," "Pokémon Blue" or "Pokémon Yellow."
Connect two Game Boy systems with a Game Link Cable. One Game Boy game must be the "Pokémon Crystal Version" and the other will be the "Red," "Blue" or "Yellow Version" or "Pokémon" containing Mewtwo. Insert the two game cartridges into the Game Boys and turn them on.
Go to any Pokecenter in both Game Boy games. You can begin trading with older versions of Pokémon after you have entered Ecruteak City in Crystal.
Walk upstairs to a nurse and confirm that you want to trade. In the Crystal Version, do not bring any Pokémon that were not in the Red, Blue or Yellow titles or the game will not allow you to trade.
Select any classic Pokémon on the Crystal game and Mewtwo in the other game and make the trade. Do not disconnect the cable until you receive a message permitting it. Save your games.