Here's my trick.

Each corner is stitched together to wrap it around the mattress. Grab the top of the two stitches along one side, and stretch them out against the mattress. If the very end of both stitches when stretched out lines up perfectly with the corners of the mattress, you've got it around the right way.

Source: have had a king bed for about 4 years and I'm pretty much only changing the sheets by myself. The difference in length of each side is barely 2 inches so it almost looks square, but this trick works every time.

You do have to have long enough arms to do it by yourself for a king though.