Travel by ferry. They are safe, regular, cheap and fun. The biggest ferry hub within the Cyclades is in Paros which has links to many islands.
Be prepared that travelling by ferry can be tedious in high season when ferries are really crowded. Usually there are two types of ferries: The ordinary ones and the speedboats hydrofoils, which are much more expensive.
Also, ferries may be cancelled due to sea and weather conditions so don't leave on the last ferry before your flight, especially if it is windy. Seas are calmer at night, so the late evening and early morning ferries are the most likely to operate.
Tickets for ferries can be usually bought from travel agencies which are located around the local port.
