In Pokemon HeartGold how do you catch Mewtwo?

Answer 1

You need to get the national pokedex and then get all the Kanto badges. Then go to Cerulian City and go to the cave where the guy was blocking the entrance.

Then you go to the bottom floor and search around. He will be there as long as you defeated red at Mt.Silver.

You can also go to Cerculean Cave and find Mewtwo, lower his HP to 1%, put him to sleep, and then throw a regular Pokeball to catch him.

You find him at Cerulean cave, but first you must beat all sixteen gym leaders. Then go to Cerulean City, go over the bridge to the north, go left, then surf immediately south until you see a cave. He is level 70 and knows really bad moves (apart from physic) so bring a dark type and he cannot do any damage to you.
Mewtwo is located in Cerulean Cave. You can access Cerulean Cave after you get all 16 gym badges.
Cerulean Cave, Kanto You Will Need: Max Repels x10 Different Sorts Of Pokeballs x? Strong Pokemon x? And Mewtwo Is Lvl 70
when you do something you will be able to go in the cave in crulen city.(in kanto).i would whatch it on YouTube so you know the path to get there.

Answer 2

Go to KANTO when you have all eight KANTO badges then go to the cave with the man standing in front of it (In the city with Misty the Gym Leader). He will let you in now. Go inside the cave to the deepest part
you have to beat all the gyms and then go to cerulean cave in cerulean city make sure u bring allot of repels , ultra balls or a master ball