Luckily, Sony did a beautiful job in making the PlayStation 4 hard drive easy to upgrade (and, according to their TOS, it doesn't even void the warranty).
Here is the step-by-step video tutorial on how to upgrade your PlayStation 4 Hard Drive:
This step by step video tutorial will guide you through the complete process of upgrading the Hard Disk on your PlayStation 4.
It features:
1. USB Drive Preparations and Software - 0:07
2. PS4 Backup Preparations - 1:20
3. Upgrading the Hard Drive - 2:30
4. Installing the PS4 Software - 4:45
Link to the official PlayStation 4 Software update:
https://www.playstation.com/en-us/support/system-updates/ps4/
If you have any questions or need any help about the procedure, please feel free to contact me.