Traveling around the Cyclades islands is generally done in boats of some form whether they be ferries, private yachts, or some smaller form of public ocean transport.  There are many ferry and boat transportation companies which operate on Naxos and its surrounding islands.

Day excursions from Naxos 

Hellenic Seaways is one of the companies offering ocean transport services.  Their boats travel to several of the Cyclades Islands.  Blue Star Ferries also travels from Naxos to several other islands.  See their websites for schedules and fare information. 

For traveling around the island of Naxos itself, both buses and taxis are available.  Many people also choose to walk when visiting Naxos Town because it is small and compact and best seen on foot.  Naxos' main bus station is in Naxos Town, with routes covering all of the island's main points.  Bus schedules:

Bus schedules on Naxos 

Taxis are available at hotels and at taxi stands in Naxos Town.