There are two kinds of cards that are used for public transportation in Korea.
A one-way ticket with no transfer costs 1,250 KRW for adults, and has an additional fee when you transfer to a different line, or use card in the case of buses. For teenagers of age between 13 and 19, it costs 720 KRW and for children of age between 6 and 18, it costs 450 KRW.
T-Money is a prepaid card, which is most widely used for public transportation.
(Example of T-money)
Price : From 2,500 won and up
Sales Locations : Incheon International Airport information desk, and online
(http://t-zone.co.kr/#link), Convenience stores (GS 25, CU, 7-Eleven, Mini Stop, With Me, Buy The Way, Story Way) bearing the T-money logo, and ticket vending and card reload devices inside subway stations.
Recharge/Refund Locations : All sales locations (*Note: The card purchase amount is not refundable) or subway station.(like bottom photo)
For more information, click here.