I value shredded potatoes, but also my fingertips. This came to me one day when I was making hash browns. Not only does it keep my blood where it should be, but I've found it to be faster as well.
Step 1: Stick a Fork in the Potato
Tines should be most of the way in.
Step 2: Shred Down to the Tines
Shred with the fork perpendicular to the grater until the tines hit the grater.
Step 3: Rotate, Repeat
Flip the potato so the fork is pointing towards you and shred the "underside" until it runs into the fork. Then rotate the potato to the next side and do the same, and so on, until you have a tiny square of potato left, which I usually just toss.