Grip the thick top of the carrot or turnip with the leaves and stems firmly in your hand, but leave the top portion directly facing you exposed. Hold the carrot or turnip so that it forms a 45 degree angle with the kitchen counter. Press the blade of the vegetable peeler against the top of the carrot or turnip until the edge of the blade pierces the surface. Pull the vegetable peeler down against the length of the carrot or turnip.
The strip of carrot or turnip skin should fall off on its own once the vegetable peeler has cut down the length of the carrot or turnip. If it sticks to the vegetable peeler, carefully pull the outer skin off the blade and discard it. Continue cutting the outer skin off the carrot or turnip by using the same lengthwise motion. Rotate the carrot or turnip in a clockwise motion as you peel until the entire carrot or turnip is stripped of its outer skin. Clean the carrot or turnip in cold water and rub your hands over the exterior. Wash the vegetable peeler using a sponge in warm soapy water. Allow the vegetable peeler to dry on a rack before putting it away.
Keep your fingers away from the blade of the vegetable peeler while you are peeling the skin off the carrot or turnip. Place one hand on the handle and the other under the carrot or turnip so that you have a firm grip without leaving your fingers exposed.