I apply a coating (ground) to a polished copper plate; with a rounded needle, I draw through the ground.
Immersion in ferric chloride etches the areas of exposed metal.*
I may also use the drypoint technique of incising into the copper.
Ink is applied, and wiped off the surface.
Between rollers, ink is transferred from plate to high-quality paper.
Unlike a cheap photo-mechanical reproduction (such as a so-called giclée made from a digital photo on an ink-jet printer – let the buyer beware), an etching is an original print because each one is inked, wiped, and printed by hand. It has a distinctively tactile ink surface and plate impression, and no two are exactly alike.
* FeCl3+Cu+H2O=FeO+CuCl3+H2