Using a London pattern anvil, anything short with a square protrusion on one end goes in the square Hardy hole at the square end and material resting on it is struck by a similar object (usually held in a long 'wire' handle) by the Smith's assistant. They are called 'sets', and come in a variety of shapes.
Taller versions in various shapes are used by the Smith alone standing (so he need not bend over) next to the anvil using a hammer in one hand. E.g a round top for dishing a plate.
Very sharp (acute) sets are used to cut off several pieces from one piece of hot stuff to save the labour of cutting bits off a steel 3x2!
My RN apprenticeship included a piece of 2" dia. steel some 9" long, one end of which was upset (fattened) and made 2" square, the other end fullered (squashed between 2 grooved sets ) to a smaller diameter. The same piece of metal followed you round the machine shop to be turned, milled, threaded, blued etc.
In all my years service I never worked iron again, but the smell of a hearth takes me straight back to 1965.