Wrap your hand around the concave side of the celery stalk so that the convex side is facing you and the leafy end is farthest away from you. Press the vegetable peeler against the celery stalk until the blade cuts into the surface of the celery stalk. Slide the vegetable peeler against the length of the celery stalk and cut away the tough outer membrane.
Carefully remove the strip of tough outer membrane from the blade of the vegetable peeler and discard it if the strip does not fall off on its own. Repeat the same process until you have peeled the tough outer membrane off the entire convex portion of the celery stalk. Clean the peeled celery stalk thoroughly in cold water. Rinse the vegetable peeler with a sponge and warm soapy water. The vegetable peeler should be dry before it is stored in a drawer.