The open beta just opened a couple hours ago and you better jump in before it closes. The fast way to get it is described as such.
Here’s how to get started:
1. Verify that your console is up to date with the latest firmware.
To check for updates on PlayStation 4
• Select the Home button in the center of the controller
• Scroll up and select Settings
• Then select System Software Update
This is required to install the Call of Duty: Black Ops 3 Multiplayer Beta.
2. Search “Call of Duty: Black Ops 3 Multiplayer Beta” in the PlayStation® Store and press X button.
3. You will be taken to the Call of Duty: Black Ops 3 Multiplayer Beta content screen. Select ‘Download’ and press X button.
I’ll see you in the beta and will have some gameplay videos later… when this thing finally downloads.
UPDATE: I was able to confirm that the Beta is only free this weekend, after Sunday you will have to preorder the game to get access. So hurry up, the download time takes forever anyways.