The following video guide is the most comprehensive step-by-step instruction on how to jailbreak your PS4. This only works for firmware 4.05 and below. If you have anything above that, tough luck. If you have anything lower than 4.55, make sure to update the firmware to 4.05 before jailbreaking, that will ensure that all the games in this site are playable on your console.
How to fully update your PS4 to 4.55 and setup the new Jailbreak exploit.
4.55 OFW Update:
4.55 Web Browser Patch: (You Can Also Use The Enable Browser Option In The WebKit Instead of Injecting from the PC!)
NetCat GUI for Payload Injecting: