it is not one of the ancients you can catch
No but you can transfer from Leafgreen,Firered to HeartGold,SoulSilver then trade to Black,White!
if you have it on HG, SS, Diamond, Pearl or Platinum yes
trade
Mewtwo is not in the game itself you will have to transfer it over.
If you somehow manage to get it on HeartGold, SoulSilver, Diamond, Pearl, or Platinum, you can trade it to Black or White using the thingy.
You can only get it in Pokemon chaos black version. Its is where mewtwo is instead of mewtwo.
You must either Poke Transfer a Mewtwo from HeartGold/SoulSilver or there is currently a Wifi Event going on for all English language Black/White games to receive a special Mewtwo for free. This event will last until March 6th, 2012. There was also a similar event occurring for Japanese Black/White carts back in 2011.
if you have the action replay
You cannot find Mewtwo in Pokémon Black, White, Black 2 and White 2 so you will have to trade for 1 or you will have to transfer it from a previous game.
I'm not sure but I think you have to complete the game and go to mystery girt and it will say Mewtwo returns click on it and there will be a guy that's wearing blue and he will give you a lv70 mewtwo im not 100% sure
mewtwo is not caught normally in black in white but you can get it off a trade or wi-fi. it may also appear in the dream world but im unsure.
So far, the events in America have been Lucario, Mewtwo, Arceus, Zekrom (Black), and Reshiram (White)