Paring, or peeling, a potato can give your final product a smoother texture and appearance. You will probably want to pare them if you are using Russet or similar potatoes, or want a final product without specks or patches of peel. Be aware, though, that much of the nutritional value of potatoes is in the skin and you will lose this by paring them.
Scrub the potatoes thoroughly under cool, running water. Even though you will be removing the skin, cleaning it can help you avoid contaminating the final product, as the knife will come into contact with both the peel and the flesh of the potatoes.
Hold one potato firmly in your non-dominant hand. Pick up the paring knife with your dominant hand.
Slip the edge of the paring knife between the potato and the skin near one end of the potato, then turn the potato while pushing the knife to peel the skin off the potato. This is similar to peeling an apple. Depending on your skill and the shape of the potato, you might manage to remove the skin in one long spiral, or you might end up with a bunch of small ovals of skin.
Put the pared potato into a bowl of cold water. This will prevent it from oxidizing and turning brown, as it would if you simply left it exposed to the air while you pared the other potatoes.
Pare the rest of your potatoes in the same way as you pared the first. Put each one into the bowl of water as soon as you are done peeling it. When you are finished, cook the potatoes in your desired manner.
You can also pare the potatoes with a vegetable peeler. Place the peeler at one end of the potato and run it along the potato to the other end, applying moderate pressure. Repeat this process until you have completely pared the potato.
Paring the potato in strips with the paring knife is another acceptable option. Simply start at one end and cut off strips to the other end, as you would have with a vegetable peeler.
Paring knives tend to be very sharp. Be very careful while paring your potatoes, as the knife could easily slip and cut you. Pare the potatoes as slowly as necessary to retain confident control of the knife at all times.