Transfer PS4 data with both consolesThis first method requires you to have both the PS4 and the PS4 Pro connected at the same time, and start by turning both on. Grab an Ethernet cable and connect the two systems, and go to Settings / System on your PS4 Pro. Look for "Transfer Data from another PS4" and follow the instructions on the screen. This requires you to hold the power button on the old PS4 until it beeps.
Select which data you want to transfer, or just transfer it all. You need to log in to all your user account on the old system to confirm that you want to transfer them, and after this the system begins the data transfer. Now just sit back and wait while the systems does the rest of the work.
Transferring data from PS4 to PS4 Pro without a network cableIf you don't have an Ethernet / network cable, you can still transfer your data, but you need an external storage device like an USB stick with a lot of storage, or an external hard drive. This storage device needs to have USB 3.0 and be formatted for exFAT (which is standard for all newer storage devices, so don't worry about formatting it).
Connect the external storage device to your old PS4 and select the "Backup and Restore" option in the Settings / System menu. Select the external storage device as your destination, and the data will transfer over to it. This will reset the old PS4 to standard settings. After this is complete, connect the storage device to your PS4 Pro and again to go "Backup and Restore". From here you can start the data transfer, and this might take a little while. After it's complete the PS4 Pro will restart, and you can begin to use it after logging into your user account. Now you need to go to the menu and select the PS4 Pro as your primary console, and you are done!