How are billiard balls made (now and in the past)?

Answer

In the past they were ‘turned’ from ivory, following the example of wooden game balls for outdoor sports. Sometimes this is still done today, with plastic rods from which balls are ‘cut’. With a lathe, a curved blade, a lot of patience and even more expertise you can come a long way, as this video shows: https://www.youtube.com/watch?v=wBsib03uHw8 (British Pathé film from 1953 about production with Alf Sorrels in London).

From the middle of the 19th century experiments have been made with the casting of billiard balls, with a wide variety of secret ingredients: cellulose, bakelite, wood pulp, hardening agents, phenolic resins. Not only the ingredients are secret, but also the construction method (cast in one piece, or two pieces that fit together) and the polishing techniques to get a perfect curve. Incidentally, the world leader in the production of (cast) billiard balls is a Belgian company, Aramith in Callenelle near Tournai: https://www.youtube.com/watch?v=jU-JgG3aVIM (promotional film by and about Aramith from 2015).

Those are just the two big basic techniques. Usually many actions are needed to get a perfect billiard ball. A perfect roundness and diameter are not even the only requirements for a billiard ball: the resilience is crucial for rebounding, the hardness is important to reduce wear on the ball itself and a perfectly even weight distribution is necessary for a straight course.