One can visit Amorgos mainly by boat as there is no airport on the island except of a helipad. Blue Str Ferries is the main transporter, as there is a daily connection from Pireaus port to the island. Detail schedule one can find at http://www.bluestarferries.gr
In addition to the big ferries, there is a daily connection with all small Cyclades by Express Scopelitis, a smaller veseal which has base on Amorgos. There also other companies which facilitate travelers depending on the season.