Knives are sharpened by grinding against a hard surface, typically stone. The smaller the angle between the blade and stone, the sharper the knife will be, but the faster it will dull. A guide is very helpful. Very sharp knives sharpen at 12-15 degrees. Typical knives sharpen at 22 degrees. Knives that chop may sharpen at 25 degrees. In short, the harder the material to be cut the higher the angle of the edge. The composition of the sharpening stone affects the sharpness of the blade (finer grain produces sharper blades), as does the composition of the blade (some metals take/keep an edge better than others).
Examples of sharpening tools are the clamp-style systems, which use a clamp with several holes with pre-defined angles. The stone is mounted on a rod and is pulled through these holes, so that the angle remains consistent. Another variant is the crock stick setup, where two sticks are put into a plastic or wooden base to form a V shape. When you pull a knife up the V, the angle is held for you, as long as you hold the blade perpendicular to the base.
Remove a wire edge (burr) if one forms during sharpening. Use a slighly steeper angle with very light pressure to do so. If not removed, it will break off in use, and the knife will instantly become dull. An alternate method of removing a wire edge is stroking from side to side on a very fine stone, using light strokes. This will flip the burr back and forth as it is ground off.
To feel for a wire edge, move your thumb lightly across the edge. It should come off with no resistance. If you feel a little bit of pull at the edge or the nail is sightly abraided, you may have a wire burr.
Traditional stones are arkansas stones, which come in soft (coarse) and hard (fine) varieties. These are traditionally used with water or honing oil, but any oil compound, including olive oil, will do. India stones are also similar to arkansas stones in function and end result.
Ceramic stones are also used very often. Unlike natural stones, they will not wear, and are very often used without any type of oil.
Water stones (both artificial and natural) come in very fine grits. They are stored in water, and develop a layer of slurry which helps polish off the edge. Generally, these are more costly than oilstones. Needless to say, oil should not be used on these.
Oil is used to lift the metal dust, called swarf, off the stone. This is usually recommended for natural stones, but some say that detergent and a brillo pad will have the same effect. Ceramic stones do not need oil, they can be cleaned off with detergent. Diamond stones should NOT be used with oil, rather, they can be washed off with water.
The best knife sharpening stones are industrial diamonds embedded in plastic or metal. These are more expensive, but still affordable. They cut about twice as fast as other stones. Also popular, and rather expensive, are sharpening blocks made from corundum.
Stropping a knife is an excellent finishing step. This is traditionally done with a leather strap impregnated with abrasive compounds, but can be done on paper, cardstock, or even cloth in a pinch. It will not cut the edge significantly, but produces a very sharp edge with very little metal loss. It is useful when a knife is still sharp, but has lost that 'scary sharp' edge from use.
Knife steeling isn't actually sharpening nor honing. All you are doing with a sharpening steel is realigning the edge. Realigning the edge goes a long way in keeping the knife sharp, as often times, a rolled edge will make an otherwise sharp knife dull. There is no reason to remove excess metal if the edge can be fixed with several strokes on a sharpening steel.
This information is taken from the Wikipedia.