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It’s a bit of a multi-step process, but not too hard. First off, make sure that you get a 2.5” HDD. I’m sure you will check, but it would be annoying to get a new HDD and realize that you got one for a desktop and it won’t fit the PS4. Once you have that, you will also need to get (or get out) a flash drive with at least 1GB of free space. Take that drive, connect to your PC/Mac and go to this Sony site where you can download the software required for a new installation of system software on your new HDD onto your flash drive: http://us.playstation.com/support/systemupdates/ps4/new-install/#installationSteps
After you have done that, get a good set of phillips screwdrivers at the ready, and go to THIS Sony website for complete instructions on removal and replacement. I’m not going to repeat the step by step instructions, but essentially you power down and unplug the system, remove the cover over the OEM HDD, remove a couple of screws and pull that puppy out of there. Then reverse the process; install the new HDD, connect the flash drive you prepared earlier via USB port on the front of the PS4, power up by holding the power button for about 10 seconds to start in safe mode, follow the instructions that appear on screen, and Bob’s your uncle.
To be honest, my concern is that a TB HDD really isn’t enough given the 40+GB of hard drive space that each game takes up, and I’m talking about the install from the disc, not digital downloads. It’s going to be a challenge for me to get used to uninstalling my games to make room for more.