Amorgos is connected by ferry boat (9-10 hours) and fast boats (5-7 hours) to Piraeus, everyday in the summer and 3-4 times per week the winder. There is also a connection with the other Cyclades islands, or you can go by aeroplane throught Santorini or Paros.
There is a relatively small road network that connects Katapola, Hora, Aegiali, Kato Meria, Mouros, Ag. Anna, Chozoviotissa monastery. There are buses every 1-2 hours. There are also taxis and rentals. To go to the other island there is net of modest roads. a large number of small footpaths suitable for journeys on foot, guiding you to wonderful locations all over the island and especially near the sea. You can find also small boats that make the tour of Amorgos or go to little islands such as Gramvusa and Nikuria, where you can fish or dive.