Each day there are two non-stop flights from Vancouver to South Korea. Flight time is around eleven hours. You will arrived at Incheon International Airport (ICN).
Once you arrived at Incheon Airport, you can either take the train, airport bus, or taxi to your destination. In my case, destination was Seoul. The most economic way is to take the Airport Railway Train and change to subway after. However, I suggest you to take Airport Bus when you leave. There are lots of stairs in the subway and I am guessing your luggage will be heavy.
Next, you can get a subway map from the information center at the arrival hall.
||$9000 Won / $7000 Won (kid)
|Train (All Stop)
|Airport Bus (Deluxe)
|Airport Bus (Standard)
If you are choosing to go with train, you need to either buy a single transportation card, T-Money, or Tourist Card.
||Fare per ride
||Where to buy
||Look for logo
||1. Subway Vending Machine
||Same as T-Money
1. Subway Vending Machine
2. 7-11; CU
On the side note, I strongly suggest you order a WiFi egg in advance and picked it up at the arrival hall.
Please check out official website for more details: http://english.visitkorea.or.kr/enu/TRP/TP_ENG_2_1.jsp