To get to the Unknown Dungeon you must first beat the Pokemon League Champion, then adventure back to Pokemon Village. After reaching the furthest point from the entrance to Pokemon Village, you will see a water path. Surf up the path, but not the waterfall unless you want to go ahead and get TM 29: Psychic. To the right you will see a path and then the entrance to Unknown Dungeon.
After getting to Unknown Dungeon it is time to enter the Unknown Dungeon. BE SURE TO SAVE THE GAME. As soon as you enter go straight up and you will encounter the famous and powerful pokemon Mewtwo!
Mewtwo is level 70.
Moves Mewtwo uses during encounter battle:
Psychic, Aura Sphere, Recover, Barrier
Catching and battling Mewtwo tips:
Mewtwo will heal so it is easier to use sleep or paralyze on long encounters
Mewtwo is faster than most average pokemon
Be prepared for a long battle if trying to catch him