Athens is the main travel hub. It’s possible to score fairly priced flights from Europe to some of the more popular islands—especially Santorini, Crete, or Mykonos—but it’s much easier to fly into Athens International Airport. From there, you can take a ferry from Piraeus Port to just about anywhere.
One of Greece’s many charms is that nobody is ever in a rush. This applies to transit as well. Airplanes and ferries are by far the most efficient modes of travel around the country, especially to the islands. On the other hand, the subway system in Athens is actually quite modern, having been built for the 2014 Olympics. It’s handicapped accessible, thanks to elevators in every station. Athens' bus system is less reliable. On the islands, buses are the way to go, unless you opt for car rental. For all schedules, check out the Greek Travel Pages.