We took the S2 train (the same one to Badaling Great Wall) bound for YánQìng [ 延庆 ]. You can just use your subway card. It costs just 6 RMB each way. Get off the final stop, which is 1 stop/20 minutes past Badaling. It took an hr and 30 minutes in total from Beijing North Station's [ 北京北站 ] ground floor by Subway Line 2's XīZhíMén [ 西直门 ] Station.
Outside Yanqing station, we took a taxi for anther 20 minutes right to the entrance of Longqingxia ( ♦ map ) [ 龙庆峡 ]. The ticket costs 40 RMB. Once you enter, you walk a bit until you reach the dam/dragon escalator, which is quite cool from the outside but just normal escalators inside.
Location: Longqingxia, Yanqing, Beijing, China