I need to produce a program that would process/read a magnetic stripe card within a windows kiosk environment and would prefer doing this in C or C++.
Could someone suggest pointers/recommendations about where one should start?

I suspect that it is connected via USB.
I have asked my user to check and await their reply.

I've never tinkered with usb so I don't know the answer to your question. The ones I have used were connected to COM port.

it could be connected to the computer via a USB port but even though that device is physically using the usb port it could be functioning as a virtual com port. If it is you can use any serial port library that is compatible with windows to read the data that is on the magnetic strip.