Complex sentence: The man goes to a psychiatrist and, after the session, the twist ending (a device which Serling became known for using) reveals the "patient" had died at Pearl Harbor, and the "psychiatrist" was the one actually having the vivid dreams.
Split into simpler sentences: The man goes to a psychiatrist and after the session the plot twist, which Serling became known for, is revealed. The patient had died in the Pearl Harbor bombings, and the "psychiatrist" was the one actually having the vivid dreams.