By ship
From the Greek mainland ferries and highspeed catamaran services (http://www.ferries.gr/booking/) run daily from Piraeus, Rafina and Lavrio. Ferrys operate to all the islands in the Cyclades, some of the larger islands also have a highspeed catamaran service. Ferry trips are four to five hours to the closest islands Kythnos, Syros, Tinos, Mykonos and Sifnos and from eight to ten hours to the furthest Santorini depending on the number of stops. The highspeeds take half the time but cost twice as much. There are daily ferries from Pireaus to all of these islands, with the exception of Kea and Kythnos which you get to from Lavrio and Andros which you get to from Rafina.
Many travelers probably consider Rafina not a possible departure port if they are heading to one of the Cyclades, but if you are arriving at the airport of Athens, you are often better off taking a ferry from Rafina than traveling to Athens and get a ferry from Piraeus.
Many boat services stop working by end of October and resume by April. Check with the operator before making departure plans as the services are subject to delays and cancellations in adverse weather.