Here is a map showing all the major roads in Koh Phangan. It is a fairly small island. It is possible to do a tour of the whole island in one day in a car or on a motorbike. Unlike Koh Samui there is no ring road going all around the coast of the island. Thus to get from Thong Nai Pan to Chaloklum, for example, you cannot do the short journey west along the coast by car (on foot it is possible); instead, you have to drive to Thongsala and then take the Chaloklum road. It is a long route and will take at least 40 minutes in a vehicle.
There are plenty of other roads and paths on the island. Many of these are barely more than foot paths and should not be attempted on scooter. The road to Than Sadet and Haad Yuan needs a 4 wheel drive and an experienced driver.
Generally speaking the roads in the west are easier to drive. It is a flatter area. This is a good part of the island to start off exploring if you are new to riding a motorbike in Koh Phangan.
The road from Ban Tai to Thong Nai Pan is now nearly all covered in concrete. There are still a few dangerous parts. This road will be completely finished in 2013 hopefully. Watch this space for road updates.
There is only one traffic light on the island. It is located in Thongsala at the start of the road to Ban Tai and Haad Rin. You must stop at the red light.