Tickets can be bought at the, literally, hundreds of travel agencies at the Pireaus port, right outside the Metro station. There are literally hundreds of ships and ferries travelling between the many islands found within Greece. From small little boats scurring between Pireaus and Aegina, Poros, Hydra and Sp tses to huge cruise ships able to transport more than 1000 cars and 3000 passengers, there are ships to serve anyone. The main islands have more than one ship per day arriving, with Mykonos and Santorini more than 6 in the summer. Some from Pireaus and some from Raf na, they usually stop in other islands along the way.
Prices are pretty similar and travellers take the first one available.
It would take about 8 hours to go to Mykonos from Pireaus which means that for the ferry that leaves at 8am, Mykonos will be sighted at about 4 pm. The general departures of the various ferries are indicated here for the summer of 1999.