You may go to the Great Wall either by train or by bus.
By train: take bus no. Te 2 from Beijing West Railway Station to chanchunjie, get off and change to Beijing Subway ,line2 to Xizhimen, then walk to Beijing North Railway Stationm to take a train (Y567 at 0933 and Y575 at 1319)to Badaling.
By bus: take bus no.83 from Beijing West Railway Station to Deshengmen, then change to bus no. 919 through or express to Badaling.

There are many sections of Great Wall in Beijing. Supposing you are going to Badaling, the most popular section, there are mainly two ways: by bus 877 or by s2 train.

Bus 877 leaves from Deshengmen. From Beijing west train station, you can take the metro line 9 to National Library, then transfer to line 4 to Xizhimen, then line 2 to Jishuitan. Upon arrival and exit from B2, walk about 500 meters to reach Deshengmen.

Or you can simply take the bus Te13 at West railway Station to get to Deshengmen. But this route may meet the traffic jam. The first route is relatively more time-saving.

S2 train leaves from Hungtudian train station. To get there, take metro line 9 to National Library, then line 4 to xizhimen, then line 13 to Huoying and then walk there. The s2 train departs about every an hour, not as frequent as bus 877.

The S2 train has been moved to Hutudian Railway Station from Beijing North Railway Station. Also, the bus 919 has been replaced by 877.