complete itinerary From Hongkong to Great wall of China August 17 to 19.

First of all, I'd like to tell you a China visa is needed for your one day tour to visit the Wall indeed. The most famous sections are in Beijing and the Badaling Section is recommended.

From HK, go to Hung Hom Railway Station to take a through train to Guangzhou East. Then take local subway line 1 to Gongyuanqian and transfer to line 2 to the South Railway Station. There take a bullet train to Beijing West.
P.S. You are recommended to book the train tickets, especially for the route from Guangzhou to Beijing.

At Beijing West Railway Station metro station, take subway line 9 to National Library and transfer to line 4 and get off at Xizhimen. Then walk to Beijing North Railway Station to take a train to Badaling.

In the way above, it seems to be a little complicated. To save trouble, you can directly fly from HK to Beijing or fly there via Guangzhou or Shenzhen. Then hire a taxi at Capital Airport to Badaling.