The forge or smithy is the workplace of a smith or a blacksmith. "Forging" is the term for shaping metal by use of heat and hammer.
A basic smithy contains a forge, sometimes called a hearth (for heating the metals; commonly iron or steel) to a malleable temperature, an anvil (on which to lay the metal pieces while hammering), and a slack tub (in which to rapidly cool, and thus harden, forged metal pieces). Tools include tongs to hold the hot metal, and hammers to strike the hot metal.
Once the final shape has been forged, iron and steel in particular often get some type of heat treatment. This can result in various degrees of hardening or softening depending on the details of the treatment.