There are two easy ways to grate carrots:  1. Use a box grater: Wash and peel your carrots before grating them lengthwise along the side of your grater with the smallest holes. Grate the carrots until it's no longer possible to grasp the carrot safely against your grater, discarding any large pieces.  2. Use a food processor: After washing and peeling carrots, dice carrots into smaller pieces so that they're easier for your food processor to grate and shred. Pulse the diced carrots until they resemble the look of thin pencil shavings.