Incheon International Airport is ranked one of the top airports in the world and is just 20 minutes by car or bus from INU's main campus in Songdo. Car and bus are your the best transportation options as there is no direct subway route to Songdo.
Taxi
Taxi is the best option to get INU. It takes 30 min and the fare is around KRW30,000. A toll, KRW5,500, to cross Incheon Bridge will be added to the final fare.
Car rental
If you prefer to drive out of Incheon International Airport, you can use the SK Rent-a-Car (https://www.skcarrental.com/) and Lotte Rent-a-car (https://www.lotterentacar.net/hp/eng/main/index.do) services. There are two car rental outlets at Exit 2 on the first floor, Terminal 1 of Incheon International Airport. Insurance is offered on all rental cars at Incheon International Airports. Cars can be reserved in advance. The campus has plenty of underground parking spaces for visitors and the fee is KRW1,000 for the first four hours or KRW5,000 for the whole day. You can find INU at Google Maps (https://goo.gl/maps/btpppYTksP9gLmq5A), but the Google Maps phone app does not give turn-by-turn directions in Korea.
Subway
It can be a little complicated to take a subway from the Incheon International Airport to Songdo as you will have to transfer from the Airport line to the Incheon line at Gyeyang Station. To buy a ticket, use one of the automated machines (KRW1,150). When purchasing your ticket, it is important to clearly state your destination. Get off at the the Incheon National University station and then walk or take the local bus/taxi to campus. Below is the subway map.