A GPS tracking device usually contains a GPS receiver and a cell-phone + sim card in order to send data to a remote location from the car, it would help to know if you think the device was 'placed' or installed in your car, a placed tracker would have to use it's internal battery which won't last very long, if the tracker was installed (which obviously takes longer), it would probably be taking power from the car's battery and therefore can operate indefinitely.
Ideally the GPS needs to be able to 'see' the sky in order to determine it's location, so unless it has an external aerial, I wouldn't expect to find it anywhere on the car where it has large amounts of metal above it, i.e. under the car (away from edges) or car bonnet etc.
Detecting the tracker would be a the same as detecting a cell-phone, there are devices you can purchase to do this but they're not cheap, which really just leaves physically looking for the device, it could be as little as 40mm x 40mm and if it has been 'installed' will have wires connecting it to the car's power supply