Here are some main routs to get to island Korcula:
There are ferry and catamaran connections. Catamaran is only for passengers, ferry takes cars.
car ferry from Rijeka
car ferry from Split to Vela Luka (50km from Korcula, bus connection)
from Split to town of Korcula (ferry and catamaran)
car ferry from Drvenik (near Makarska)-Korcula
car ferry from Ploce – Trpanj – Orebic)
car ferry from Orebic (15 min ferry)
from Hvar (catamaran, only passengers) It starts from Split.
car ferry from Starigrad on Hvar to town of Korcula
from Dubrovnik (by bus or by ferry to town of Korcula)
bus from Zagreb/Zadar/Split/Sarajevo/Beograd/Mostar
with plane you can land in Split or Dubrovnik