Fresh ginger is a hassle to deal with. I process and freeze it in huge batches so I always have it ready when I need it.
Process:
If you have large pieces of ginger, cut them into smaller pieces - about 3 inches. Trim off any excessively dry or hardened edge bits. Put the ginger in a food processor and pulse until it is minced. Use a tablespoon or melon baller to scoop out portions of ginger, packing it with your hand. Turn the scoops out onto a sheet tray or plate. Freeze in a single layer. Once frozen, transfer to a plastic bag or container and store in the freezer.
Tips:
You do not need to peel ginger. (Although you do want to cut off any areas where the skin is really dry or thick.) If you do want to peel it, use a spoon to scrape the skin off.
Freezing the scoops of ginger in a single layer ensures that they freeze in individual pieces. When you need ginger for a recipe, you can grab a piece and add it. Easy as pie!