A container with a sealing lid or a plastic zip bag
Peel the ginger. Freeze the small pieces as is. Slice or julienne the big pieces.
Wrap the sliced or julienned ginger in small 5 x 6 cm or so pieces of plastic wrap. (There's no need to wrap each portion up tightly. The plastic is just to divide it up.)
The whole bits can be grated when they are still frozen. Sliced ginger is good for simmering fish, julienned ginger for Chinese dishes, and both are used for Japanese dishes.
Put the ginger in a storage container with a tightly sealing lid and freeze. The julienned ginger will freeze in bundles, but can be used as-is.
Story Behind this Recipe
When I buy a bag of ginger, I always let some of it get moldy or go bad, which is a waste. So whenever I buy a whole bag, I like to cut it all up and freeze it.
You can save some time and effort when you're cooking. It seems that some people chop it up finely and freeze it, but in our house we use julienned ginger the most. If you freeze julienned ginger, if you leave it out for a bit at room temperature, you can chop it up easily even if it's still a bit frozen.