From Dongdaemun History & Culture Park Station take Line 5 (blue line) towards Gwanghwamun and get off at Gwangjang Market Station. Total ~15 mins train ride, 5 mins walking to Gyeongdong Market.
Walk 15 minutes (1.2 km) to Jongno 5-ga Station, subway Line 1 or Line 5, 5 minutes to Gwangjang Market Station, then 5 minutes walk to market entrance.