How do I get there just the fastest way?
Here are the cheapest airlines that fly from all major airports favorable to Athens, via the respective link you can directly search for your desired flight dates because you will be immediately on the homepage of the lowest bidder.
Comprehensive search engine for cheap flights
Athens with www.aegeanair.com
Athens with www.germanwings.com
www.easyjet.de flies Berlin - Athen
And of course Olympic Air
The way always leads naturally to the travel agency you trust. And there they usually offer you a cheap flight to Athens. Or you book yourself right directly in the Internet ;-)).
From Athens you fly with either a small plane in 35 minutes to Naxos or you can choose one of the many ferries or high-speed boats that need to Naxos for the 185 km between three and six hours. Most recently, there is also a very fast ferry from Rafina to Naxos see here: http://naxos-holidays.de/index.php/en/journey/from-airport-to-ferryboat
In three and a half hours a Flying Cat brings you comfortably to the island and to/from Rafina you get even faster than to Piraeus.
Tickets from Rafina online at: Hellenic Seaways (Highspeed Ferries),
Don’t have any concern about the way from the airport to the port of Athens, public transport is very well organized. You come easily by bus or train ride to the center of Athens, Piraeus or Rafina.
We have compiled the most important information on a separate page. Click here! http://naxos-holidays.de/index.php/en/journey/from-airport-to-ferryboat
In the summer season charter flights also fly to Athens or to Santorini and from there is a rapid transfer (1 to 3 hours) guaranteed to Naxos.
Mykonos you should not fly because the ship connections to Naxos are only irregularly and at least make one expensive night in Mykonos or Paros necessary.
Certainly not the fastest journey from Northern and Central Europe to Naxos, but so memorable: the train over the Alps to Ancona.
From there you can make a twenty-hour boat trip to Patras (already a small cruise), from Patras you need then another two hours to Piraeus. From Piraeus to Naxos directly.
There are also ferry connections from Venice or Trieste to Patras. The boat connection there but usually takes 2 days. The best way to drop by the ADAC directions: http://www.adac.de/reise_freizeit/reiseangebote/faehren/faehren_neu.aspx?ComponentId=104157&SourcePageId=11175
They give even discounts when you are a member; only in German.
How to get to Naxos with its own aircraft, did kindly wrote for you one of our dear guests.
But if you are looking for a bargain or your travel agent preferred to sell to Turkey, we have put together a few addresses here:
Info about ferries: