It is possible to buy a used car from a private dealer and not know that it is equipped with a GPS tracking device. For the most part, you will want to remove the tracking device just to be careful. It is illegal for somebody to track you without your consent, but it never hurts to be extra safe. A GPS tracker may be intricately intertwined with your car's electrical wiring, so having a mechanic do a thorough inspection of your car may be adequate enough to locate the device. If you want to do it yourself, you will need to have a radio frequency (RF) detector.
Park your car in a place where it is unlikely that any other GPS signals are being sent out. Store security, traffic lights, security cameras and other car's GPS systems can all send out signals. If you can drive to a remote campsite, or around a lake or river, you shouldn't encounter any other GPS signals.
Plug your RF detector into your car's power source and set it to continuously detect outgoing signals. Signals from a GPS tracker can be sent out every few seconds or every 20 minutes. The longest you will likely wait to detect a signal is 20 minutes. That is if you turn on your RF detector right after a signal has been sent out.
Wait until the RF detector detects a signal. If no signal is detected with a half an hour, there is either no GPS tracker in your car, or your RF detector isn't functioning properly. If you detect a signal, you have concluded that there is a GPS tracker in your car and you will have to find it by hand.
Sweep your RF detector around your car until the detection signal gets stronger. This will help you find the tracking device. The problem is you might only get one signal every 20 minutes, so you could be there for a long time.
Search the entire inside of your car. A GPS tracking device could be as small as a matchbook, so you will have to check thoroughly. You may have to take apart some pieces of your car before you find the tracker. It could be in the door panels, the steering wheel column or even the dashboard. Make sure to check the seat cushions, underneath the mats and pedals, and in the boot.