Directions from Seoul by Subway (the cheapest way):
Travel by subway to Sangbong station. The way I did this is by taking the Gyeongui-Jungang line from Ichon station.
At Sangbong station, transfer to the Gyeongchun line.
Then, travel by train to Cheongpyeong station.
At Cheongypyeong station, walk about 10 minutes to Cheongpyeong bus terminal.
From there, take a bus (20 minutes)to the Garden of the Morning Calm (they don't have numbers, just look for the one for the Garden (아침고요수목원)