I want to travel to the Great Wall by bullet train in half a day. How to organize?

Jose, the easiest way is to catch a taxi from your hotel to Beijing North Railway Station. It costs around CNY 20. Then you can catch S2 train from there to Badaling section. Or you can walk around 100 meters to find Sitongqiaonan bus station. There you can take bus no.26 to get off at Xizhimen station. Then you can walk to Beijing North Railway Station.