You can get there only by ferry. Apart from the national carrier Jadrolinija (jadrolinija.hr) there is also a private company "Mediteranska Plovidba" which serves 3 times a day a line from Drvenik (mainland) to Domince (near Korcula city) and this route is the cheapest and short. There are also long-distance Jadrolinija ships stopping in Korcula centre.