I wear it with the screen on the inside. I tried on the outside, as that is how I would wear a normal watch, but the orientation of the screen and the placement of the buttons makes it feel unnatural to not only read but also to manipulate the device.
As for which wrist to wear it on, I was taught when I got my first watch as a child to wear it on my non-dominant hand. I'm right-handed, so I wear mine on the left. I was not told the logic behind this concept, but one thing I've noticed with the Band is that I'm not nearly as comfortable pressing the buttons and using the touch screen with my left hand as I am with my right hand.