Can you connect a Playstation or xbox controller to a laptop that you can play with?
Yes you can.
How does it work? For example if I want to play fifa
You can check on yt.
Yes, just like any other controller.
I think you have 2 options. 1. Test whether you can connect the controller to your PC in the settings, 2. You take a program like DS4Windows with which you can use your controller. But first try the settings