Use the endless free access points or
Use a Korea Telecom 3,000 won per hour pre paid card that you can only purchase at Seoul airport, but the login software does not work on my computer, or
Use a Internet Bung (cafe).
Most public buildings and the airports I passed through had at least one free wi-fi service, and while one hotel charged for wired access from my room, it did provide free wi-fi in the lobby. At another extreme was a hotel that provided free wired LAN to the room and wi-fi access in the lobby. For the most part I could find free and pay wi-fi everywhere and often – they often coexisted in the same locations!