Trains from Bergen auf Rügen, Binz and Stralsund. A change may be necessary at Bergen or Leitzow if arriving on a long distance train. The train station and bus station are next to each other, and only a short walk to the town. There is a bus link to/from the Ferry Port (for Sweden). If using the regular Sassnitz - Binz bus service for the ferry, the nearest stop is in Dubnitz (after the turning to the port, at the top of the hill, if traveling from the Binz direction). It will seem quite a long way from this stop to the terminal if you are backpacking!
Frequent buses to Binz and other Rügen towns. Beware that, on rural services, changing from one bus to another seems to be popular — the driver will announce "umsteigen (placename)".
There is a supermarket along past the shops, turn to the left if you've come down through the pedestrian street from the train/bus stations.