For the purpose of this article, let's assume that your favorite knife has come up needing a sharpening. You can tell easily enough. It won't slice that tomato without first stabbing it with the point, your roast crumbles under the blade, you have to apply a lot of pressure to cut through the softest food, and you can't remember the last time it was sharpened.
If it is not quite that bad, maybe all you need is the knife applied to a sharpening steel. This turns the edge of your knife back to its true alignment. The micro teeth are formed in the original shaping of the edge. With use, the micro teeth get turned over, and pushed out of alignment, thus a dull edge. The steel removes very little metal, it just pushes the teeth back into alignment.
To use the steel, hold it by the handle in a vertical position, with the point resting on a folded towel to protect your countertop. Hold the knife at approximately 22.5 degrees to the steel, and starting at the heel of the knife, draw it downward and pull it towards yourself, until the point of the knife, and point of the steel converge close to the towel.
Do equal alternating strokes per side. If the edge is not too bad, it should only take a few strokes to true it up. If the knife gets used a lot, the steel should be applied before each use. Remember that half of 90 degrees is 45, and half of that is 22.5 degrees. Keep that picture in your mind to find the correct angle.
A knife that has been thrown around in a drawer with all the other kitchen gadgets, may need a little more work. This is where a sharpening stone, or electric type sharpener gets put to work. The electric sharpeners need little explanation, they come with instructions. The use of a stone is another matter.
Put in simple terms, you want to maintain the same angle, 22.5 degrees, and pretend you are taking a thin slice off the stone. The same principal applies to the number of strokes, keep them even on both sides. I start at ten strokes per side, and reduce it by one stroke after both sides are done, and keep counting down to one per side. If this is not enough, keep the final strokes to one per side, until the desired edge is accomplished.
There are several types of stones in use. There may be specific instructions with each type of stone, and they should be followed for safety reasons, ease of use, and satisfactory results. If all else fails, take your knives to a qualified professional sharpening facility.
In any case, keep your fingers away from the edge, apply a little pressure, be patient, and enjoy the downtime from the hustle and heat of the kitchen.