The Incheon International airport which is the largest main international airport in Korea is the nearest airport to Korea University.
If you wish to come from the Incheon International airport by subway, it takes about 75 minutes and cost 4,050 KRW per person. You can get in to the train at Incheon Airport Subway station (line 1) and transfer to line no. 6 at Geongduk station and then get off the train at Korea University station. Find more information at Seoulmetro http://www.seoulmetro.co.kr/en
If you wish to come from the Incheon International airport by bus, you can take airport limousine bus (No 6101 or 6102) at the airport bus stop and get off at Sungrye Elementary School bus stop which is the nearest bus stop to Korea University. It takes about 105 minutes and cost 15,000 KRW per person. Find more information from http://www.calt.co.kr. If you wish to come by a taxi, it will cost about 50,000 KRW and 90 minutes to come from Incheon International airport to Korea University.