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Etching is the process of using strong acid to cut into the unprotected parts of a metal surface to create a design in intaglio in the metal (the original process - in modern manufacturing other chemicals may be used on other types of material). As an intaglio method of printmaking, it is, along with engraving, the most important technique for old master prints, and remains widely used today.

Modern Technique in detail
A waxy acid-resist, known as a ground, is applied to a metal plate, most often copper or zinc but steel plate is another medium with different qualities. There are two common types of ground, hard ground and soft ground. Hard ground can be applied in two ways. Solid hard ground comes in a hard waxy block. To apply hard ground of this variety the plate to be etched is placed upon a hot-plate, a kind of metal worktop that is heated up. The plate heats up and the ground is applied by hand, melting onto the plate as it is applied. The ground is spread over the plate as evenly as possible using a roller. Once applied the etching plate is removed from the hot-plate and allowed to cool which hardens the ground.
The second way to apply hard ground is by liquid hard ground. This comes in a can and is applied with a brush upon the plate to be etched. Exposed to air the hard ground will harden. Some printmakers use bitumen as hard ground, although often bitumen is used to protect steel plates from rust and copper plates from aging. After the ground has dried the artist "smokes" the plate, applying a flame to the plate to darken the ground and make it easier to see what parts of the plate are exposed. Afterwards the artist uses a sharp tool to scratch into the ground, exposing the metal.
Soft ground also comes in liquid form and is allowed to dry but it does not dry hard like hard ground and is impressionable. After the soft ground has dried the printmaker may apply materials such as leaves, objects, hand prints and so on which will penetrate the soft ground and expose the plate underneath.
The ground can also be applied in a fine mist, using powdered rosin. This process is called aquatint, and allows for the creation of tones, shadows, and solid areas of color.
The design is then drawn (in reverse) with an etching-needle or any other sharp pointed tool such as a dentist’s pick. After completing the drawing by carefully scratching into the plate, exposing the clear metal underneath the plate is then completely submerged in an acid that eats away at the exposed metal. Copper plates and zinc plates are often dipped into ferric chloride solution and steel plates are dipped into nitric acid. The strength of the acid determines the speed of the etching process. The etching process is known as biting. The waxy resist protects the acid from biting the parts of the plate have not been exposed. The longer the plate remains in the acid the deeper the "bites" become.
During the etching process the printmaker uses a bird feather or similar item to wave away bubbles and detritus, produced by the dissolving process, from the surface of the plate. If a bubble is allowed to remain upon the plate then it will stop the acid biting into the plate where the bubble resides.
The plate is removed from the acid and washed over with water to remove the acid. The ground is removed with a solvent such as turpentine. Turpentine is often removed from the plate using methylated spirits as turpentine is greasy and can affect the application of ink and the printing of the plate.
The entire plate is inked.
A piece of matte board, a plastic "card", or a wad of cloth is often used to push the ink into the incised lines. The surface is wiped clean with a piece of stiff fabric known as tarlatan and then either wiped with newsprint paper or some printmakers prefer to use the blade part of their hand or palm at the base of their thumb. The wiping leaves ink in the incisions. You may also use a folded piece of organza silk to do the final wipe. If copper or zinc plates are used plate surface is left very clean and therefore white in the print OR many artists leave a slight film of ink over the entire surface or selected areas to produce a warm “plate tone”. A damp piece of paper is placed over the plate and it is run through the press.

Printing
Printing the plate is done by covering the surface with ink, then rubbing the ink off the surface with tarlatan cloth or newsprint, leaving ink in the roughened areas and lines. Damp paper is placed on the plate, and both are run through a printing press; the pressure forces the paper into contact with the ink, transferring the image onto the paper. This process is then repeated each time for a new print. Unfortunately, the pressure also subtly degrades the image in the plate, smoothing the roughened areas and closing the lines; a copper plate is good for, at most, a few hundred printings of a strongly etched imaged before the degradation is considered too great by the artist. At that point, the artist can manually restore the plate by re-etching it, essentially putting ground back on and retracing their lines; alternately, plates can be electro-plated before printing with a harder metal to preserve the surface. Zinc is also used, because as a softer metal, etching times are shorter; however, that softness also leads to faster degradation of the image in the press.

Artists
There have been etching masters in ALL periods of time from the time of Durer to the present. Rembrandt is considered by most as the foremost etcher in history but other illustrious names include Van Dyck, Callot, Goya, Meryon, Whistler, Renoir, Mary Cassat, Picasso, Seymour Haden and the American Joseph Pennell. A large proportion of ALL fine artists in the past have also worked with etching or other printmaking mediums.