The Blue Star Ferries are modern and fast and have regular daily schedules between Athens and the islands throughout the year.
Hellenic Seaways provide a fast hydrofoil connection and regular ferries between Athens and the islands.
SeaJets have a regular schedule in the summer from Piraeus to Naxos as do Nel Lines from Lavrio
For all ferries and highspeeds it is advisable to book well in advance
on-line during the summer months.

Olympic Air several daily flights from London to Athens and a daily flight from Athens to Naxos. Book well ahead in advance if possible.

British Airways has regular daily flights to Athens and seasonal flights to Santorini.
Aegean Airlines
Norwegian Airlines
Air Berlin

Easy Jet
A good alternative is to take a charter flight to Santorini.
There are regular daily ferry connections between Santorini and Naxos.

On arrival at the new Athens airport you can take the Express bus (E96) for 3 Euro to the port of Piraeus.
There is also a new Metro connection from the airport to Athens and to the port of Piraeus.