Learning how to use a knife sharpener is a basic technique all cooks should learn. Much as we warn children to stay away from knives because they are sharp, cooks stand in much greater danger from dull or unevenly sharpened knives. Dull knives require greater hand-pressure to produce results, which makes you more susceptible to slipping. There are two kinds of hand-held knife sharpeners: a double set of sharpening rings, and a straight or rounded pumice or metal rod, often called a "cook's steel."
Using a double-ring knife sharpener
Check your knife to be certain it can be sharpened manually. Knives with serrated edges are factory-sharpened and are not suited to this method. Knives with heavily-waved edges, such as bread or frozen-food cutters, will produce uneven results when manually sharpened and are best done professionally. A smooth even blade is needed for good manual sharpening.
Grasp your double-ring sharpener by its handle. If you are just learning to use it, rest it on a counter or cutting board (holding both sharpener and knife in the air is a quick path to injury until you've had lots of practice).
Draw the whole knife blade toward you through the gap between the two sets of rings (from the part closest to the handle to the tip). Keep the ring-assembly flat on the board and the knife perpendicular. Apply enough pressure that you hear a friction sound, but do not bear down hard--pulling the knife hard through the sharpener will actually dull or damage the edge. Three or four pulls are usually sufficient. Lift the knife after each pull and repeat. Do not push the blade back through the rings.
Wipe sharpening residue from the knife blade with a paper towel (some cooks prefer a dab of oil on the towel, to protect a carbon-steel edge, but water does as well). Place the knife blade flat on the counter or cutting board and wipe each side with the towel.
Using a pumice or steel sharpener
Use this for plain-blade knives only. Grasp the handle of the sharpener. Hold the sharpener facing away from you, pointing slightly down. Grasp the knife handle in the other hand and stroke the blade edge down the sharpener. The blade should be at a slight angle to the sharpening rod. If in doubt, hold it so that you could insert a finger between the top of the blade and the rod, with the bottom edge of the blade in contact with the rod.
Draw the knife blade down the rod in a single stroke, beginning with the edge closest to the handle and ending at the tip. This takes a little practice, and you've done nothing wrong if you run out of sharpener before you run out of blade. Your goal is to keep the knife blade moving so that the sharpening strokes are diagonal to the blade, not straight up and down. Start with a short blade, like a paring knife, and work up to your longest carver. Especially if you have a carbon-steel knife, which is prone to darkening and rust, you'll be able to see little shiny diagonal lines on the sharp edge--that's just right. On a stainless steel blade, you'll see the shadow of gray sharpening dust. Repeat three to five times until you've sharpened the whole edge.
Apply steady pressure with your strokes but, as with the other sharpener, resist bearing down hard.
Turn your knife over to sharpen the other side. Grasp the sharpener and knife as before. This time you will be stroking the blade toward you. This stage is more challenging, and you may want to move your fingers back on the sharpener handle. Set the blade at the same angle as before and slowly draw it toward you, from the edge near the handle to the tip. Two to three strokes is sufficient. Wipe the knife with the towel.
When you watch a professional cook sharpen a knife, it looks as though he is working very hard. Not so--he is just going faster than you do. A slow, careful job does just as well as the theatrical flash-and-slash--and may produce even better results! Antique stores and yard sales are good places to find an old-fashioned "steel," a household essential when the Sunday roast was a weekly event. Older steels designed for domestic use often feature a guard-plate between the handle and rod, which gives you much more confidence in handling large knives.
Resist the impulse to check your work with your fingers--we've all done it, and we're all sorry. Do this alone in the kitchen until you are confident of your skills. Sharpening a carving knife at the table is a ritual, not a requirement--ignore if it makes you nervous.