You could freehand a drawing, but I think it's smarter to work out your design on paper first. Create a paper template by using your fingers to rub and crease a sheet of plain copy paper onto the interior circle of the plate. Trace this interior depression with a pencil, then cut out the circle.
Tape your paper onto the front, or the inside, of the plate — you know, where your food will go — with the drawing facing down. Once it's secure. flip over the plate so the bottom is up.
It's hard to tell from this photo, but the paper drawing is taped underneath the clear plastic.
Now all you gotta do is draw, using oil-based markers. If you make a catastrophic mistake, use a cotton ball and nail polish remover to wipe off the marker ink. It works like a charm!