Any guesses as to how this magic trick was done?

Japanese magician makes a styrofoam cup and a lit cigarette float. http://www.dailydot.com/unclick/japanese-magic-floating-trick-smoking-room/

He’s using invisible thread that you can get at any reputable magic shop.

You can definitely see that that the cup is dangling from something. When he switches to the cigarette, you can see him carefully manipulating the thread around the butt and he then goes on to make it appear to levitate.