
You have 2 main options.
1. PS4 Extended Storage USB HDD
Format a USB HDD on the PS4 as Extended Storage and then install or move the games to that.
This is the easiest and most simple method.
On the PS4 go to Settings > Devices > USB Storage Devices > Select Your USB Drive > Format As Extended Storage
2. AppToUSB
Format a USB HDD as exFAT and use stooged's AppToUSB.
This is a more complicated method but instructions can be found on the PS4 AIO Guide here. (look for 'USING APPTOUSB')

Pros and Cons:
PS4 Extended Storage - Pros:
Easiest method to setup and use.
The USB drive can be plugged in to another exploitable PS4 and the games will work on that PS4 console.
(if you are using the USB drive on more than one PS4 you must make sure that you run HEN before you plug in the USB drive.
This does not matter if you are ony using it on one PS4 console)
Works with both legal games and backups.
PS4 Extended Storage - Cons:
Once formatted as external storage, the USB drive cannot be used to tranfer files to and from a PC anymore.
If you plug the drive into a PC the drive/files will not be visible.
AppToUSB - Pros:
Because the USB drive is formatted as exFAT you can still use the same USB drive on a PC.
The installed games on the USB drive are in .pkg format and are an identical copy of the .pkg file you used to install the game,
so basically you have a backup copy of the .pkg file on the USB that you can use to re-install the game if needed.
AppToUSB - Cons:
Harder to set up for beginners. (although if you follow the guide you will be fine)
You must install a new game to the PS4 first, then transfer it to the USB drive with AppTo Usb. You cannot install a new game directly to the USB drive.
When the PS4 was fist exploitable the official method of using Extended Storage on USB did not work that is why AppToUsb (and similar payloads) were created.
With the release of HEN v1.7 Extended Storage on USB was fixed and the official method of using Extended Storage on USB now worked as it should.
In my opinion, the only advantages that AppToUsb has now is that the drive is still usable with a PC and the drive can act as a backup of your installed .pkg files if you need it.
I personally now use the Extended Storage method if my internal drive is full and have another USB drive to use for transfering files to and from the PC if needed.
I also have another drive that I use keep a backup of all my installed .pkgs so I can re-install them if needed.