For both American Truck Simulator and Euro Truck Simulator 2, all types of controllers work on Windows as long as they are DirectInput (PS2/4 and other unlicensed peripherals) or XInput (Xbox 360/One licensed only).

The Logitech Driving Force GT falls under the DirectInput category so is compatible. The only thing is that you need to configure it in game for it to work.

Will I just plug it in and it must work with the game immediately or do I have some installations/configurations to make it work?

With American Truck Simulator and Euro Truck Simulator 2, you need to configure all of the controllers at least once.

How will I know it does work?

For both American Truck Simulator and Euro Truck Simulator 2, all types of controllers work on Windows as long as they are DirectInput (PS2/4 and other unlicensed peripherals) or XInput (Xbox 360/One licensed only).

For the Driving Force GT, Wikipedia lists ATS and ETS2 as compatible.