There are quite comfortable airport shuttles called Airport Limusine Bus directly from the arrival area of Incheon (Seoul) Airport.
Just go out the arrival and look for the Airport Limousine counter. There are some inside the hall and some outside. Although you can pay at the end of the ride directly in the bus it is better to pay the ticket in advance. First you do not need Korean Won and second you can ask for the right bus. They speak English at the counter inside the arrival hall.
The current bus schedule you may find here.
Because the enormous distance to the city Taxi cabs are pretty expensive. The bus is really affortable and fast.