How to catch Mewtwo - Pokemon Red and Blue

Firstly you need to defeat the Elite Four.

Starting in Cerulean City, you need to travel north up the Nugget Bridge, then West and Surf South and round to the West. Here is the enter to Cerulean Cave. You need to make your way to the bottom floor of the cave. If you still have the Master Ball use it, if not you need to stock on Ultra Balls. It would be wise to get an Escape Rope as well as you don't have to climb back up the cave floors.

Mewtwo is originally a man-made Pokemon created to be the Strongest Pokemon ever to have lived. It was being held on Cinnabar Island but destroyed the Research Facility and fled to Cerulean Cave to be alone. Mewtwo is a Psychic Type. It is weak to Bug. Its moves are; Barrier, Psychic, Swift and Recover. Recover can be annoying, healing it HP when it is low, Barrier will raise its Defence and Swift will never miss and Psychic is a strong Psychic-Type Attack. If you have low-levelled Pokemon, it is worth thinking about having some of the Legendary Trio on your Team just to bulk out your Team and to take hits.

Mewtwo