The normal way to lay at night is with the lower end up against your shoulders. I've attached two pictures of the correct way to sleep in the pillow.
You can actually lay your head on the top of the butterfly (where it comes to a point) of if you want to stretch out your neck and relax your spine. I wouldn't recommend sleeping on that side, that would just be useful for therapy. It's designed to use from all sides.
The traditional sleeping position is the butterfly wings by your shoulders.
Common Pillow Positions