You need a PlayStation Plus membership to play PlayStation 4 games online--but not this week if you live in Europe or Australia. Sony has announced an open multiplayer event where you can play online without a subscription.
This runs November 15-20, and there is nothing else required of you like signing up for something. Online modes in any game should simply work. So far, this has been announced for Europe and Australia, but there is no word as of yet regarding the United States.
From the official wording, it sounds like this free PS Plus event does not allow you to download November's free PS Plus games. You'll need an actual membership for that.
PS Plus subscriptions, which costs $60/year, grant owners the ability to play online, discounts on store content, and free games delivered monthly. A PlayStation Plus subscription is required in order to continue playing the free games Sony provides. Once a subscription lapses, access to the library of free games is rescinded.
The timing of the free PS Plus offer comes not long after the launch of Call of Duty: World War II and right before the release of Star Wars: Battlefront II on November 17.