If you fly to South Korea without tourist guide then you should do some homework before your departure. Otherwise your trip will end up with sad memory and disappointment.
When you are at the arrival level of Incheon International Airport, look for the notice board which displays airport map to determine your location.
In case you need any assistance, feel free to proceed to the information counter. The Korean girls on duty are pretty and polite. They would like to ensure you have a pleasant stay in South Korea and bring back sweet memory. It wouldn't be any problem to communicate with them because they speak fluent American English.
South Korea provides world first-class public transport service. You can travel by bus or rapid rail from Incheon International Airport to South Korea capital, Seoul. It takes around one hour by bus from Incheon International Airport to Seoul.