With its peppery, intense taste, fresh ginger is best when you grate it into very small bits. Any type of kitchen grater works for ginger, with some doing the job more effectively than others.
The procedure for grating ginger is the same regardless of the type of grater you use:
Hold the ginger in one hand with your fingertips and the grater in the other hand.
Rub the ginger back and forth along the grater.
Use your fingernails to hold the ginger if you haven't cut a large enough piece to get all the ginger you want.
Discard any large, errant chunks or the last remains of ginger that you can no longer hold.
Scrape off the ginger that adheres to the back and front of the grater with the tip of a paring knife or a metal spoon.