Cut the whole apples in half and peel off the skin using a peeler. Remove any blemishes on the surface.
Cut the peeled apples again - you will get apple quarters.
Hold the apple in your left hand (if you are right-handed). Take a sharp paring knife in your other hand. Carefully cut the apple roughly in half below the core. Then turn the apple piece and make the same cut on the other side until you have cut out the whole core.
Place a hand grater in a larger bowl or on a cutting board. Grate the peeled, cored apple pieces on the side with the larger holes.
Notes
The knife has to be well sharpened so that it slides into the apple's flesh without unnecessary pressure. A sharp knife helps control the depth of the cut.
Apples turn brown or oxidize after grating. This is nothing harmful; brown apples may only not look appetizing. To prevent apples from browning, drizzle them with freshly squeezed lemon juice after grating.