To get the character Mewtwo in the "Pokémon Crystal" video game, the player must either trade for him using the Time Capsule or obtain him via an event. He cannot be caught like other characters in the game.
The Time Capsule allows a player using "Pokémon Crystal" to trade characters with others using a first generation Pokémon game, or with his or her own copy of such a game. The first generation games are "Pokémon Blue", "Pokémon Red" and "Pokémon Yellow." Additionally, in Japan, "Pokémon Green" is part of the first generation. The save file in the first generation game must have Mewtwo in order to trade him into "Pokémon Crystal".
Nintendo, the game's publisher, also gives away characters to players at official events. This is the only other official way of obtaining Mewtwo in the "Pokémon Crystal" game.