Amorgos is the long, mountainous island at the south-eastern edge of the Cyclades, known for its dramatic cliffs, old walking trails and the Hozoviotissa monastery built into the rock face. From Piraeus it is a long way out, about 173 nautical miles or roughly 320 km, and the direct ferry is a day's journey on the conventional ships.
The first thing to know is that Amorgos has two ports. Katapola, in the south, is the main harbour and gets both companies' boats; Aegiali, in the north, is served by Blue Star Ferries only. They are far apart by road, so choose the port closest to where you are staying rather than simply the first sailing you see.
Blue Star Ferries carries this route through the year on three or four days a week, on large conventional ships that stop at several islands on the way. Journey times vary a lot with the routing, from about 5 hr 25 min to over 9 hours. In the warmer months, Seajets adds high-speed boats to Katapola that can make the trip in 4 hr 35 min, on up to every day in high summer, but at a much higher fare: from €79.70 in Ferryhopper's table, against €43 for Blue Star.
Because there is no daily conventional service and no airport on Amorgos, the crossing takes some planning. Pick your port, check which days sail, and in summer book early, especially if you want a cabin on one of the longer Blue Star crossings.