The closest airport is "Alexander the Great" airport about 20 km from Kavala. Planes, mostly touristic charters, fly all over Europe.
Air Berlin  will operate every Monday and every Friday from 2 May 2008 to 31 October 2008 (Flights to/from Berlin, Hamburg, Dusseldorf, Frankfurt, Munich, Nuremberg, Vienna). Aegean  (Flights to/from Athens daily)
By regional coach
Interurban coaches ("KTEL" buses) are by far the most convenient way to travel around Greece, as well as for intra-regional travelling. There is frequent bus service from Athens Kifisos Station to Xanthi, as well as from Thessaloniki bus terminal "Macedonia" to Xanthi.
Trains OSE  connect Xanthi to other cities in Greece. Travelling with ordinary trains can be cheaper, although a little bit slower, whereas choosing a fancy faster Intercity train will cost the same amount of money, or even more than a KTEL bus.