There are a few variants.
First one is the quick and dirty web based VPN that you just use in your browser. There are millions of free websites that work more or less. It's basically trial and error. You basically just visit their website and surf through them to the websites you like.
Then there are some that will require a client on your PC. Some of them cost money, some are free and some have free trials. With that kind of client all of your connections will go through that VPN including games and other apps.
Depending on your router there is also the possiblility to set up a direct VPN from your router to a VPN service. Those are also usually paid. I wouldn't recommend a free one for this as some of the less proper ones will just spy on your connections.
Don't forget, when you use a VPN provider every single one of your connections will go through a single point and can be read by the VPN provider and whoever he chooses to share this data with. As far as I know the privacy laws for private VPN providers aren't as strict as for your normal ISP.
To get your PS4 through the VPN you will have to either have a client on your PC and then route your PS4 through it or establish a VPN with your router.
I don't have any control over my router (shared accommodation), so how would routing my PS4 through a PC client work? And also, any that you'd recommend?
I don't use VPNs and I probably never would, so I cannot recommend any.
The basic premise of routing your PS4 through your PC would be to just use the IP of your PC as the default gateway in the PS4 network configuration. In theory your PC should just act as a router by default. There might be additional settings necessary depending on your OS. Things like firewalls, anti virus can be an issue here. Next possible point of failure could be the VPN client itself. Depending on how it works it might or it might not be possible to route other IPs other than your own through it.
I'm sure it can all be made to work, but it might require some tinkering.