Since the late 1700s, small shot (up to about 3.8mm as a maximum) was usually made by pouring molten lead through a sieve at the top of a chimney-like tower (a process patented in 1782). The sieve broke up the stream into small droplets which then formed spheres as they dropped from a height into a cold water tank at the bottom. The shot was then sorted by tipping it onto a slightly inclined table and anything that didn't roll down the slope went for re-melting. In 1848 a patent was filed for the addition of a cold air blast that shortened the height of the drop required.
Before these processes, shot was usually made by dribbling the lead directly into cold water without first free-falling in a tower (poor quality of roundness, but cheap) or in moulds (good quality of roundness, but expensive). Larger shot was usually made by cutting lead sheet into small pieces and barrel-tumbling them until they were round.