You may take AREX train (airport line) and then transfer to subway line 4 (blue line).
Although you may not take the last express train which departs at 22:28, you may take the commuter train because the last train departs at 00:22 for Seoul Station (首爾火車站).
At Seoul Station, transfer to subway line 4 (green line) and get off at Dong Dae Mun Stadium Station (東大門運動場站) or Dong Dae Mun Station (東大門站).
The fare is 4200 Won from Incheon Int'l Airport to Dong Dae Mun.
However, when you arrive at Seoul Station, it should be around 00:20 or later. There might be no subway. You have to go out of Seoul Station and take a taxi. the taxi fare to Dong Dae Mun should be around 10,000 Won or less.
2007-12-27 04:40:28 補充:
Sorry. At the moment, the airport train only runs to Gimpo Airport (金浦機場) and the last train might be at 23:46.From Gimpo Airport, you have to transfer to subway line 5 (purple line) to Dong Dae Mun Station (東大門站). If there is no subway, you may try to find the local bus or take a taxi.