This article explains how to connect a PS3 controller to a PS4 console. The instructions are for official Sony DualShock 3 and SixAxis controllers only. Other PS3 controllers may not work with the PS4.
How to Use PS3 Controller on PS4 *EASY METHOD*
You’ll need a special controller converter to use a PS3 controller with your PS4. Sony doesn’t make such adapters, so you’ll need to purchase one from a third party. Some adapters, such as the Gam3Gear Brook Super Converter, are designed to connect PS3 controllers to your PS4, while others let you control multiple controllers with multiple devices. The former are generally less expensive than the latter. Each adapter comes with instructions and connection cables, and most require you to download additional software.
The Cronusmax Plus Cross Cover Gaming Adapter, available from Amazon, is an excellent choice as it supports scripts that allow your PS3 controller to do everything a PS4 controller can.
Before you begin, you'll need to unpair any PS4 controllers that are currently connected to your PS4 console.