The standard rules apply. The difference is that you can see only 1/2 of a shpere at any given moment!
The idea of a round chessboard fascinated me to the point of exploring with other shapes.
When the limits of two dimensions were broken, I stumbled on the idea of a sphere.
Using an old metal globe of the moon, I hand painted the 64 `squares' on it's surface,
leaving the poles blank; as is the center of the circular chessboard. I then fashioned
a pedestal on which to mount it. Magnetic chessmen came in very handy here. Play is unique,
in that the `board' must be rotated to view the locations of all of the pieces.