The airport railroad
Early in 2011, the airport railroad opened up, connecting Incheon Airport with Gimpo Airport, the hongdae area and ending at Seoul Station, which in turn connects Seoul to the rest of the country. Look for signs in the airport pointing out the airport railroad or ask for directions at the numerous information kiosks.
Riding the full length, including and transfers prior to entering the airport railroad (provided you complete your transfer within 30 minutes) should cost roughly W5000 ($5). This means you will end up paying about half the price of a bus ticket. See T-Money card for more information.
If you are taking the Airport Railroad from the city centre to the airports, then yu can board at Seoul Station, which also links to Lines 1 & 4 of the subway. The entrance is well posted and is found close to Platforms 12 and 13 in Seoul Station.
It can also be boarded from various other stations in Seoul. See map for more information.