How to get to different islands in Greece; book a hotel in advance.
The best way to the Greek islands is by boat. They are cheap and relaxing with restaurants, snack bars and beautiful scenery. The boats to the far Greek islands like Crete, Rhodes, Lesvos & Kos leave in the evening. With a cabin it's like going to sleep in a hotel and waking up in a new place. Frequency of boats varies from island to island. To get to the port of Pireaus from Athens take the metro from the stop closest to you (probably Monistiraki or Omonia) to the last stop: Pireaus. The boats are across the street. There is a map on the dock that tells you where to find the ferries for each island. If you don't have a ticket you can buy them at the boat too though if you want a cabin you should get it in advance. Also if you are traveling to the islands on the days preceding Easter and the 15th of August or any Friday in July and August you should buy your tickets in advance. The same goes with returning after those dates and on Sundays.
Finding reliable ferry info on the Internet is like finding an 8 Karat diamond in a gum machine. The schedules are changed so often that webmasters have had nervous breakdowns trying to keep up. Even travel agents have to phone the ferry companies to make sure the boat is running. If you want to be sure then use a travel agency to book your hotels and let them worry about the ferries.
Important: Not every island is easily accessible from another. You must keep in mind when planning your Island itinerary that moving from one island chain to another can be difficult and in many cases you will have to return to Athens to do it. Generally travel within an island chain is easy but for example going from Santorini to Lesvos is nearly impossible without going back to Athens. It is best to have this information before making plans. However the reliability of any Greek ferry Schedule is suspect and if you are planning on going to more than one island I suggest working with an agency. They will have access to better and more up-to-date information. If you are backpacking, staying in campsites or booking a hotel when you arrive and not particular about where you stay then it won't matter though in August you may have problems finding a hotel room.
Of course you won't have to worry about the ferry if you have your own boat.
They say it's the one essential Greek island and Santorini should not be missed. Take the ferry and sail into a giant volcanic cauldron that is as dramatic, or more so, then the Grand Canyon. Most people stay in or near Thira where the nightlife is or Oia where it is a little quieter and go to the beaches by bus, car or bike in the day. Others stay on the beach and go to Thira at night or to watch the sunset. Maybe the most sensible thing is to stay in the village of Akrotiri, which not only has a view of the volcano but also is within walking distance of the beach. The sunsets in Santorini are like nothing you have ever seen before and for that reason many honeymooners want to stay in a hotel overlooking the volcano in Thira or Oia. But if you are a family with children this may not be practical since not only will you have to get your crew to the beach every day but also you won't sleep easy with your kids playing on the edge of a 1000-foot cliff. A car is useful but not essential because there are buses and taxis.