Andong is most easily reached by bus from Seoul or Daegu. Express buses run from Seoul's Gangnam Bus Terminal to Andong several times a day, with a journey time of about 2 hours 40 minutes. From Daegu it's about an hour and a half by express bus. The intercity bus terminal is in the centre of the city and within walking distance of most accommodation.
By train, Andong sits on the Jungang Line, though the service is slower than the bus. From Seoul's Cheongnyangni Station the journey takes about three hours. The KTX high-speed rail does not serve Andong directly; the nearest KTX station is Gimcheon Gumi, from which you would change to a local bus or taxi.
Andong does not have a civilian airport. Daegu Airport is the nearest, about 80 km south, accessible by bus to Daegu and then onward by express bus to Andong.