Dubrovnik Airport: There is no Korčula airport. In season, a pre-booked shared minibus/direct transfer from DBV to Korčula Town is the least-fussy option: roughly 2¼–3 hours, usually about €30–45, with the Pelješac crossing included. Do not assume a same-day Dubrovnik ferry connection will line up after a flight. The cheaper DIY route is airport bus into Dubrovnik, then a scheduled catamaran to Korčula Town when one operates; it is only good if the timetable happens to work.
Split Airport: Take the airport bus or local transfer into Split ferry port (about 30–45 minutes), then use a direct catamaran to Korčula Town when scheduled: the sailing itself is about 3 hours and is usually around €25–35. This is excellent only on a day with a direct sailing—often an afternoon departure. With a car, use the Jadrolinija ferry to Vela Luka and allow another hour by bus or taxi across the island to Korčula Town.
Orebić ferry terminal, Pelješac: This is the practical mainland gateway if arriving by car, bus or private transfer from Dubrovnik. Take the passenger ferry straight to Korčula Town: about 20 minutes, generally frequent in season, and only a few euros. Drivers should use the car ferry to Dominče instead; it is about 3–4 km from the Old Town, so factor in the final drive, taxi or walk.
Vela Luka ferry port: Use this mainly for vehicle ferries from Split. It is not Korčula Town: allow about 1 hour onward by island bus, longer if the connection is poor. It is a sensible car route, not the elegant foot-passenger arrival.