Well, in the comic books, Ant-Man shrinks thanks to the technology developed by Hank Pym. The Pym Particles interact with his body and change his molecular structure to reduce his size.
Ant-Man shrinks using a special suit with Pym Particles that manipulate his size.
Ant-Man's ability to shrink in the comics is enabled by a concoction of scientific advancements and Pym's genius. The suit he wears is infused with Pym Particles that essentially reconfigure his physical form to make him smaller.