Much like Zygarde, Mewtwo won't be available to catch until after you beat the Elite Four. Once beaten you'll be able to gain access to a cave that was previously blocked off at the location Pokémon Village. You'll just have to use Surf to cross a small river and voila.
The beauty is that Mewtwo is literally waiting inside, ready for battle, which means no long, drawn out exploration is necessary here.
Mewtwo will be level 70 when encountered and as we all know by now, he's a Psychic type so prepare wisely. Also Save your game prior the to the fight!
If you've already used up your Master Ball on previous Legendary Pokémon, just make sure to stock up on a lot of Ultra Balls, as well as necessary healing items just in case. Having a Pokémon with the ability False Swipe will also ensure you don't knock out Mewtwo by mistake.
Once caught, depending on the version you're playing, Mewtwo will be holding either Mewtwonite X or Mewtwonite Y which will allow him to transform into one of the two version specific Mega Evolutions.
