How is a gable vent attached to vinyl siding?
FWIW, it is a typical install for vinyl siding.
This could be installed in 2 different ways. Either way the vent or portion of the vent is installed before the siding goes on.
First way, a base plate or ring that will hold the grille/vent is nailed in place first. It defines the shape of the vent, and provides the means to hold the finished part that shows in place. This allows for easy cutting and installing the siding with the proper expansion gaps around the base of the vent.
The second way, it goes on as a one piece unit, with a nail flange just like the first one, that gets hidden by the siding, but this one will need to have the siding place into the groove around the perimeter, making it a bit more difficult to install.