How do we get from Xicheng district, Beijing to Mutianyu Great Wall?

Xicheng District covers a large area. Since you didn't tell your location, it is quite hard to give you specific information about which public bus or subway line you should take. But you can take a taxi to Dongzhimen Tansport Hub from Xicheng District, first. Upon arrival, hop onto bus no. 916 to Huairou North Street and then take a taxi to the Wall at a cost of CNY50~60.
For return trip, you can walk 500 yards to MTY Roundabout to take bus h23 to Huairou North Street and then transfer to bus no. 916 to reach the city proper.