PlayStation 3 games do not work on the PlayStation 4. The system does not offer backwards compatibility for disc-based games from any prior Sony console.
Sony does offer a cloud-based emulation system called PlayStation Now that offers backwards compatibility with select PlayStation 3 games. These games must be re-purchased as PlayStation Now titles and streamed to the PlayStation 4 console over an active Internet connection, as the emulation is done on the server side.
As of 2014, this cloud-based service is available in North America as an open beta with a limited selection of titles. The beta is not currently available in other markets.