By Flight from Seoul / Busan
It's only in Korean and I'm afraid you need a Korean friend to assist you for booking the ticket. It's a budget flight like AirAsia.
How to make Korean friends? Try Couchsurfing. I have personally couchsurfed myself. View my experience here and here.
Korean Airline - http://www.koreanair.com/
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Korean Airlines and Asiana Airlines are more expensive than Jeju Air.
Go to Mokpo/Wando/Incheon/Busan and take a ferry from respective ports
Seoul to Mokpo
Seoul Express Bus Terminal - Mokpo Terminal (every 30~50 minutes/4 hour 20 mins trip/17,600won~28,800won)
Seoul to Wando
The journey is around 5 hours 40 minutes. Seoul dwellers can head to the Express Bus Terminal (line 3, 7, 9) to start their journey to Wando-gun (W33,000).
There are 2 types, Express buses and Inter-city buses which often have separate terminals. Express buses can be either first class (udung) or second class (chikhaeng). Express buses are non-stop except for rest stops of 10 minutes every 2 hours. Inter-city buses stop to pick up passengers.
The Seoul Express Bus Terminal (02-782-5551/2) is on Seoul City Subway Line 3, south of the Han River. It has buses departing to Jeonju, Busan, Daegu, Daejeon, Ulsan, Incheon and Gwangju.
Dong-Seoul bus terminal (02-458-4852/4) on Seoul City Subway Line 2, near Kangbyon station, has buses to Jeonju, Incheon, Gwangju, Busan, Daegu and Daejeon.
Seoul Train Station/Yongsan Station to Mokpo Station
Saemaeul train - 4 hours 30 mins, 36,600won
KTX - 2 hours 50 min, 40,500won
Seoul to Busan
KTX trains connect Seoul to Busan via Daegu and Daejeon in about 175 min (₩51700). Other trains, such as Saemaeul and Mugunghwa, connect Busan with other major cities as well. They're cheaper but slower than KTX. Head to the First Class car for a free-of-charge water vending machine.
Busan Port - More info from Life in Korea
Wando Port - More info from Lonely Planet
Recommended to use Internet Explorer 7.0 for opening the all the Korean websites mentioned.
Fare for train/subway/bus/ferry/flight might change.
Labels: How-To, Transportation