Instructions
Play through "Pokemon Leaf Green" or "Fire Red."
Defeat the Elite 4 and fix the network machine on Island 1. Fix the Network Machine by collecting the ruby on Island 1 and the sapphire. For the sapphire, you must find Team Rocket in the Island 4 cave and follow them to Island 6 and then to Island 5. Upon defeating them on Island 5, you will get the sapphire.
Go to the Unknown Dungeon in Cerulean City.
Explore the cave. At the end of the cave, on the lowest level, you will find Mewtwo.
Battle Mewtwo and capture him using a Pokeball.
Save your game.
Start "Pokemon Platinum" with "Pokemon Leaf Green" or "Fire Red" in the Game Boy Advance slot of your Nintendo DS or DS Lite.
Play through the game and defeat the Elite 4.
Go to Route 221 and enter Pal Park.
Talk to the person at the counter in Pal Park to select Pokemon from your copy of "Pokemon Fire Red" or "Leaf Green" that you would like to transfer over to "Pokemon Platinum." After selecting Mewtwo, you will be given Park Balls which have a 100% catch rate.
Head into the Park to locate Mewtwo. Mewtwo is in the "Field Area" of Pal Park. Mewtwo's location will be random, so keep walking around the field until you encounter him in battle.
Capture Mewtwo by throwing a Park Ball at him.