How do you get Mewtwo in Pokemon Fire Red?

Answer 1

Beat the elite four, go back to where Misty's city is. There is a road north, go up it. The is water at the end surf it once you get to a cave opening, there will be a cave and you search for Mewtwo

Better Answer:

You have to beat the elite 4 and then, you have to get the national pokedex from professor oak (must have caught 60 different pokemon) then you go to one island and talk to celio(he will ask u to get ruby and a sapphire for him)

Ruby: the ruby is located in mt. ember. when u get to the top, u have to go to the right and u should see 2 rocket grunts. battle them and go into the cave.

(the HM Strength is required)

once u have the ruby, take it back to celio and he'll give u a rainbow pass i think to travel to the sevii islands.

Sapphire: go to the dotted hole on six island. go up to the door and use cut and the door will slice open. when u get in the cave, follow the following directions to get to the gem

up, left, right, down.

once u reach the sapphire, a scientist will come and take it and leave. leave the dotted hole and go to the rocket warehouse. once u get there, u will have to get through the maze. once u get to the female rocket grunt on right (just ahead of where the entrance is) battle her and then she'll change one of the arrow panels where u can go out and go back in without going through the maze. then u go up to another rocket grunt. battle the grunt and then go up again and you will see the scientist that took the sapphire. battle him and he'll give u the sapphire. get out of the warehouse and go back to celio.

once u gave the sapphire to celio, u can go back to the kanto region.

When u get back, go to Cerulean City and go up onto the nugget bridge and surf down to where u see a cave. (where a guy was standing) go inside and find mewtwo.

hope i helped.