Years ago, when I was taking a lithography class we had to grind the image off the stone so we could put on a new image. We sprinkled on a little carborundum, positioned another stone on top (those things were heavy) and ground the top stone over the bottom stone in a figure eight pattern. At the time I did not understand why we were using a figure eight pattern. All I knew was that it took "hours" at the sink getting the image off.
When sanding the side of a ring or the bottom of a flat piece of metal clay a figure eight pattern is used to keep the piece flat and even. (So that's what we were doing!) A circular motion can be used, but it's best to keep rotating the position of the piece as there is a tendency to push harder on one side. Rotating the position will counter this tendency.
I don't do this on the back of a flat piece, since the back often has high and low spots. For a flat back I sand directly on the back side with my finger so the sandpaper goes into the spot and keeps the shine consistent.
I was thinking of this as I was working on a necklace for my Granddaughter. The CZ was set using the ball method which needed to be sanded down. (She is four so I was keeping it simple and wanted to try out one of my new Christmas cookies cutters.)
The picture is after firing and before brushing. For anyone not familiar with metal clay, this is what the silver looks like when it comes out of the kiln. It is not a white coating but the silver particles standing up on end. Once they are brushed with a brass brush they lie down and the silver shows.