How to get to this island.
A number of ways, I will detail the two routes I have taken.
Fly to Santorini (Also called Thira) Stay there a couple of nights, you really must experience the Chora (main town - all main towns are called "Chora" - it just means "The place").
It's brash, vulgar - and unmissable. I stayed in Karterados, it's an easy 20 minute walk from Chora but rooms are much cheaper.
Get the bus to the port and take either a regular ferry or the Flying Dolphin - which is dearer but faster - direct to Naxos. Up to you. Check the timetables first. You can buy tickets in advance at any travel agent.
Fly to Mykonos. As before, bus to the port and ferry as per above. Naturist beaches on Mykonos as well.
Another way (I've not done this) is to fly to Athens and get a ferry from Pireaus.
Go to Naxos page for the beach guide.