The easiest way to get Seoul after you get to Incheon airport, had been Limusine shuttle. But now we have Airport metro, which is a lot faster and cheaper transportation.
It costs 13,300KRW (=$13) for express which takes 43 minutes to Seoul Train Station, or costs 3,700 KRW (under $4) for regular which takes 53 minutes.
It drops from Incheon to Kimpo domestic airport, Seoul Digital Media City (Where you can transfer to Metro #6 line), Hong-ik university (Where you can transfer to Metro #2 line), and Seoul Train Station (Metro #1, #4 Line).
If your destination is around City Hall, you have two choice. You transfer to #2 line at Hongik university to get City hall station, or stop at the final station and get Taxi (should cost under $5)
Other transportation : http://visitseoul.blogspot.com/2007/07/how-to-get-in-from-incheon-airport.html
Seoul Metro Map : http://cafefiles.naver.net/data10/2005/6/13/78/subway_seoul_eng.jpg (this map doesn't show you Airport metro)