Firstly, if you want to follow a car, then do it in a car that won’t get any attention. For example following someone in a flashy, bright red car is not a bright idea. Choose a car which no one will notice.
The second most important thing to remember is to maintain a safe distance from the car you are chasing, because you do not want to spook the driver. If s/he notices that you are following him or her, s/he might speed up and get away. The objective is to stay behind or even cross the car a few times, so that you don’t raise any suspicions.
You can always tag the other car with a GPS, which will allow you to track it beyond visual range. This is probably the best way to track a car without getting caught.
Make a team of trackers and divide the distance among them. This way, when one car covers the mileage that it is supposed to, the other driver in another car can take it up from there and continue to follow the target. This trick is practiced by many enforcement agencies all over the world. In this process, the targeted driver can never guess that he or she is being followed.
When following a car, always wear shades to hide your face - this will make you look inconspicuous. Also remember to not honk the car horn to get people out of your way, as this will draw attention to you and you might be spotted by the driver you are following.
Never over-speed when following a car, as you do not want to be pulled over by the police for crossing the speed limit.
Do not stop for refreshments as this might let the target get away. Always keep your eyes on the car that you are following. Do not use indicators when turning, as these might get noticed by the target.