The key to trailing car lights is long exposures (slow shutter speeds). For this the camera will have to be held steady (on a wall or tripod).
For best result use the cameras self-timer to trigger the exposure (or use a remote triggering device) to eliminate camera movement when the shutter is released.
Once you have set this up select Shutter priority mode (Tv on a Canon) and dial in a shutter speed of 4 seconds the camera will select an appropriate aperture setting. Take a few pictures and examine the results. Then just experiment with different shutter speeds... longer will give longer trails etc..
oh yeah and when you get some good ones you need to post them on this forum