Question: how to connect a brand new ps4 controller to your ps4?
Answer: Make sure that the PS4™ system and TV are turned on. ... 
Connect your DUALSHOCK®4 (micro USB port located on the back) to your PS4™ (USB port located on the front), using the USB cable that came with your PS4™.
While the DUALSHOCK®4 and PS4™ are connected, press the PS button on the controller.