Naxos can be easily reached from Piraeus, where there are daily ferries going to the Cycladic islands.
If you want to check the ferries from and to Naxos and order a ticket - click here.
Naxos has an airport for for domestic flights and can also be reached by plane from Athens with Olympic Air (national flights only because there is no international airport). The journey takes about 45 minutes. The earlier you book the cheaper it is. Sometimes you have to be fast because tickets seem to be sold out quickly. If you book early it is a little bit more expensive than going by ferry, but you save yourself a lot of time (the bus ride to Piraeus of almost one and a half hour and the time on the ferry).