To get Mewtwo in HG/SS, you must do multiple things first.
First, you must get all Kanto Badges.
Next, go to Cerulean Cave, you must go deep into the cave to get to Mewtwo.
If you have any trouble, I've put some maps from Bulbapedia to help you out. (You may have to zoom in, the maps are small.)
3F (Room with Mewtwo.)
Hope this helps!