The first thing you need to do is format your hard drive. So, connect your hard drive to your PS4 using a USB cable. If you have problems with the PS4 recognizing the hard drive like I was, make sure you're using a USB 3.0 cable and not the now-ancient cable that likely came with your DualShock. Once it's connected, you just need to hop into your settings:
Head to Settings > Devices > USB Storage Devices and select your external hard drive.
Select Format as Extended Storage and tap X.
Select Next and tap X.
Select Format and tap X.
Select Yes and tap X.
Select Okay and tap X.
From here on out, any new game or software you install will be located on your external hard drive. Save data and image/video captures will stay on the internal hard drive.