The tail lights on the car in front of you are there to warn you what they are doing/planning on doing. When they start indicating you can predict what is coming, the car will drift over the same side as the indicator, slow down and maybe stop (depending on traffic). Finally they will turn in the direction of the indication.
You then should check your mirrors, especially for bikes, and start to slow down. If clear, drift over to the other side of the road in preparation to pass them, check the road markings and oncoming traffic and if safe to do so pass the turning vehicle.
The other tail lights to watch for are the Brake Lights, simply put, when these go on the car in front is slowing down.
Your response to this should be to check your mirrors and ... wait for it ... slow down. While it does sound so obvious and simple you'll be amazed how often people don't seem to get this one.
The best and safest drivers look ahead, they will manoeuvre the car so they can see through other car windows or around the car altogether. They are looking for what the cars two or three spaces ahead are doing. When they see brake lights come on up there, these drivers know that every car in front of them will be doing the same. They'll check their mirrors and come off the accelerator, these drivers don't usually need to brake as often as others because they will lose speed naturally in advance of the upcoming hazard because they saw it coming.
These drivers will see the traffic lights ahead and have a rough idea of what colour they will be when they get there and they will adjust their driving accordingly. You'll spot these ones because they seem to slow down for no apparent reason, but if you look ahead you might just see a red light. In time these drivers get used to the length of different lights and will usually just roll up as they turn green.
All that said DON'T trust that an indicator definately means they are turning that way, don't assume that a Green Light means everyone has stopped for their Red Light. Always keep watch, always check one last time.