Ferries from Athens to Greek IsIand and back operate daily. Depending on the vessel and the route, you can choose fast or normal Boat.

Piraeus and Rafina are the main ports that serve ferries from Athens and back. In the summer, there are also ferries from, Rafina port which is close to some of the Cyclades Islands.
These Ports connect to most islands of Cyclades.

Dodecanese Island is possible to reach them only from Piraeus Port which is the main Port of Athens.

The Ionian Islands you can reach them from Ag. Konstantinos Port or Volos
In summer, there are also occasional ferries to islands Crete( Heraklion Port or Chania Port)  which you can reach them only from Piraeus Port

Between island, there are many connections especially during the high season which can give you the option to connect a variety of islands