Hold the ginger in one hand, and, using an upside down spoon in the other hand, scrape the thin skin off the ginger. Place the peeled ginger in a plastic bag and freeze until solid.
Place a fork on the countertop on its side. Take a piece of frozen ginger and scrape it across the tines of the fork. The ginger will fall into tiny pieces. Presto! Grated ginger!
Notes
A microplane is perfect for this job if you own one!