To clarify, you will want to get onto the AREX All-Stop Train. This is located in the basement on B1 level. After getting your bags from baggage claim, you will head to the arrival hall. Then take the escalator or elevator down to B1 and walk towards the trains. You will see signs for AREX. Just be aware that AREX has two kinds of trains. One is the All-Stop Train, this is the one you want to take. The other is the Express Non-Stop Train. This will take you directly to Seoul Station without stopping anywhere. You can purchase the tickets at the station if you do not have a T-Money card. Btw, T-Money card can also be purchased at the convenience store such as 7-11.

Another option is to take one the Airport Limo bus. Bus #6002 will take you to Hongdae station. It is the 3rd stop. Cost is 10,000 won but the benefit is that you will not have to carry your luggage up and down countless escalators going to and from the station.