Unfortunately, Sony took a leaf out of Microsoft’s book for the worse when they announced that online multiplayer on the PlayStation 4 would be gated behind a paywall: you would need a PS+ subscription to access it. And while I am sure there were a lot of people who were unhappy with the decision, they also had no choice, and had to just deal with it.
Thankfully, Sony also seems to have taken the good with the bad here- just as Microsoft offered free multiplayer weekends to Xbox Live Silver members, so too will Sony be offering a free multiplayer weekend this week to everyone. So, from January 16 to January 18, no matter whether you have PS+ or not, you will be able to play your PS4 games multiplayer online.
Notably, only online multiplayer will be made available to non PS+ members- other PS+ benefits, such as the free games, or cloud storage, will still be unavailable to you unless you subscribe, so just keep that in mind.