Watch this fascinating video from The Discovery Channel or just read this:
The 2-piece modern ball is formed by surrounding a spherical molded core made of rubber or synthetic rubber with a hard covering.
The core is then situated in an injection mold. Extremely hot plastic, made of surlyn or usually urethane, is injected and forms a hard, dimpled coating around the core.
The ball is painted, stamped with a logo, given a glossy coat and dried. Three-piece balls have a core center, a rubber covering of the core and a final coating.
Polara Golf makes both 2- and 3-piece golf balls.
The rubber covering may be rubber string wrapped around the core.
4-piece balls have another covering over the first covering around the core that's not as hard as the final coating but not as soft as the rubber covering the core. The manufacturing process varies a bit in the exact composition and materials used, based on different manufacturers and whether the ball is made for distance or control.