For the PS4, you connect the USB and Optical Audio cable from your PS4 to the wireless Base, go into settings on the PS4 under sound and audio and change your audio to Optical and select dolby digital (if DTS is selected remove that). That should give you Dolby game sound and chat on the PS4 wirelessly. For some games I recommend using the chat cable from the headset to the controller, but it is sold separately. Also, make sure that under devices for headsets you have output to headset set to chat only, not all audio.
For the XBox one, I would believe the connections from the system to the base would be the same (USB and Optical Audio to wireless base), but you will need to purchase the XBox One headset adapter to get the mic to work.