My first and foremost occupation is as a die engraver.  The dies I cut are usually soft steel which are then heat-treated (or hardened) for use in the medallic industry.  Uses for these dies include coins, medals, medallions, keytags, plaques, metalware, etc.  The two methods I use for die-cutting are pantographing and hand die-cutting.  A pantograph machine is based on a ratio principle.  A pattern or template, one or more times larger than the die being cut, is used as a guide to reproduce a design in the die.  As a stylus follows the pattern, a cutter is repeating the same motion in the steel die.  If the pattern is 3 to 1, the die being reproduced would be 1/3 the size of the pattern.  The other method for cutting dies is hand die-cutting.  This is done by using chisels, gravers, punches, and a flex shaft with burs to create the die.  This method is more suitable for modeling, or for a sculpted look.  The two methods can also be used in combination.  Since dies are essentially a negative image, the design must be cut in reverse.  Pieces reproduced from them will then be positive images.