The simplest way is the Korean Air Limo Bus #6702. If you're flying Korean Air you can buy tickets on board and get a slight discount when you buy the round trip. One way is 15,000W.
Otherwise, when you come out onto the arrivals level, go to door 4A or 10B. Whichever you are closest to... Nearby you will see a ticket window and tell them Grand Hyatt Itaewon. There's another Park Hyatt in Gangnam, NOT the same obviously. Then look for the bus sign posted nearby. The men managing the bus lines are also very helpful for foreign tourists.
If you take the airport train, you have to transfer to the subway and a local bus which isn't always the easiest with big bags. Cost is around 5,000W for the train. If you have a T-Money card, you can transfer to the bus for free. If not, you have to pay another 1,300W on the bus.
Just stick to Korean Air Limo bus.
https://seoul.grand.hyatt.com/en/hot...portation.html