Here's the deets straight from Kevin Kelly on the offer, to quote:
That means you can engage with the storyline in the campaign with “Rising Threat” and “Black Sky,” the first two levels of the game. Plus, you can jump into multiplayer with friends and foes (Level Cap of 15), and try to hold your own against the undead in a zombie infested 1980’s amusement park (Level Cap of 3).
What’s even better is that if you purchase the game, your progress and experience will carry over. You can find all the details below, so get set to enjoy Call of Duty: Infinite Warfare.
How to Participate
To access the Call of Duty: Infinite Warfare Free Trial, go to PlayStation Store and search “Call of Duty: Infinite Warfare Free Trial.” You will be redirected to the Free Trial Product Page. You can also access the Trial on the Infinite Warfare game page under the “Demos” category.
PlayStation Plus is required for Multiplayer and Zombies in Spaceland. Please note that the trial is the full game with restricted access, and you will need around 60 GB to download the full experience.
If you decide to purchase the full game, you will not need to download Infinite Warfare again. Availability for the Infinite Warfare trial will vary by territory. Please check your territory’s first party store for availability information.