There are certain ways to come to Naxos:
From Athens International Airport "Eleutherios Venizelos" there are several direct flights on a daily basis (flight duration: 30 minutes).
Santorini & Mykonos islands' International Airports operate and handle several flights from many European cities. From there transportation to Naxos or any other of the Cyclades islands is operated by ferries & speedboats.
From Pireaus port ferries (trip duration: 5 1/2 hours), speedboats (trip duration: 3 1/2 hours) & catamarans (trip duration: 3 1/2 hours) are operating at morning and evening hours.
From Rafina port (which is closer to Athens International Airport) speedboats & catamarans (trip duration: 3 1/2 hours) are operating on a daily basis