For foot passengers there is year-round daily catamaran service between Korcula town and Hvar town. From October 1st to May 31st it leaves Korcula at 6:00 Monday through Saturday and at 13:00 on Sunday. The return trip leaves Hvar at 17:10, 7 days per week. From June 1st to September 30th it leaves Korcula at 6:00, 7 days per week. The return trip leaves Hvar at 18:10, 7 days per week. The journey between the two islands takes about 1.5 hours. You can view the full schedule here: Korcula to Hvar Catamaran.
For those traveling with a car, there are no longer any direct ferries from Korcula to Hvar. You will have to take a car ferry to Split and then switch to a car ferry to Hvar (or travel to the mainland via the Korcula to Orebic ferry and drive to Split or Drvenik to catch a car ferry to Hvar). There is twice daily service from Vela Luka (on the island of Korcula) to Split departing at 6:15 and 13:45 from June 1st to September 30th (view schedule here: High-season Schedule). From October 1st to May 31st there is also daily service from Vela Luka to Split, but the times vary depending on the day of the week. Here is a link to that schedule for more details: Low-season Schedule.
Once in Split there are several car ferries per day from Split to Stari Grad on the island of Hvar. The schedules for those ferries are as follows:
Foot passenger ferries generally do not need to be booked in advance but reservations should be made for car ferries. Reservations can be made and tickets can be purchased at Jadrolinija offices throughout Croatia and through specific travel agents in Europe & Australia, as listed on the Jadrolinija website.