Do you see the figure turning clockwise or anti-clockwise?
I found this post from a blogger, Averal. Basically, if you see clockwise, then you use your right brain. If you see anti-clockwise, then you use your left brain. For more explanation, vist her blog and look for the post dated 30 Oct 2007.
I found a way to 'switch' directions. Just focus on the shadow on the legs, then bluff your brain into believing that the legs are rotating in another direction. It took me a while to get it right, and after that, switching was an ease. I guess it's also a good exercise to switch your brains. Maybe you should watch this animation and force yourself to switch to that desired direction in order to use that part of your brain. For instance, if you are undecided about something, and you want to think logically, then look at the animation and force yourself to see the anti-clockwise.
Updated 11 Dec 2007: some readers still think that the animation above is fake, that is, the animation actually changes direction on itself. I've attached a screenshot of the animation sequence here. Click to see. There are 34 frames in this animation and it loops. So whether the dancer turns left or turns right depends on how your brain sees it. This is no trickery: only your brain is tricking you.