Pokemon
¤ Red and Blue
¤ Red and Green (Japanese)
¤ Blue Version (Japanese)
¤ Yellow Version
¤ Gold and Silver
¤ Crystal Version
¤ Ruby and Sapphire
¤ Emerald Version
¤ FireRed & LeafGreen
¤ Diamond and Pearl
¤ Platinum Version

Universal Information
¤ What is this section?
¤ Breeding Pokemon
¤ Evolution Methods
¤ Elemental Types
¤ Pokerus Infection
¤ Shiny Pokemon

Affiliates
¤ Amity Square
¤ Dark Eon Hideout
¤ Eevee's Headquarters
¤ Eevee's Mansion
¤ Jenviousity
¤ Lugia's Island
¤ Perfect Absolution
¤ Pokemon Battle Dome
¤ Pokemon Inferno
¤ Pokeshore
¤ PokeTech
¤ Pokeuniverse
¤ Pokemon Valley
¤ Sapphire Milotic
¤ The Spriting Shack

In FireRed and LeafGreen, Mewtwo is still located deep within the cavernous Cerulean Cave, which is to the northwest of Cerulean City. The cave is home to some of the most powerful Pokemon in the game. So powerful are these Pokemon that the location of the cave (seen in the image above) is not even on the map.

In the originals, you could access this cave once you defeat the champion. This time, however, you cannot access the cave until you do a few tasks first.

The first task to get into this cave is the same as in the originals: conquer the Elite Four. After which you must obtain the National Dex. Once you do that, you must get the machine on Isle 1 operational with the Ruby and Sapphire plates. After that, the man blocking the entrance will move.

Before going inside, you should bring along your most powerful Pokemon, plenty of restorative items, and many Ultra Balls.

Once you enter the cave, you'll need to go up and surf at the water. Keep surfing until you reach the end (if you surfed from start to finish, you'd make an odd "U" shape.)

Go right from here, up the stairs, head right, then left, down another set of stairs, and then to a ladder.

That ladder will take you one floor up. On this floor, go left. When you see an opening to go down, follow it. You'll come to a three-way fork. Take the right-most path, and you'll find a ladder leading down. Follow it, then the next ladder; you'll be on the last floor which is pretty straight forward.

At the end, at level 70, is Mewtwo.

The best way to fight him would be to just throw the Master Ball you got in Sliph. If you wasted it, I would suggest you put him to sleep or freeze then wail on him until he has almost no health left, at which point you throw Ultra Balls until you capture it. You can capture him with this method; I've caught him with a Pokeball once.