If you are now in Beijing or Shanghai, then the cheapest way to get to Hong Kong is to take train. Nowadays, it’s very convenient for tourists to go to Hong Kong from mainland China by train through the Jingjiu Railway.
Located in Yau Tsim Mong District, Kowloon, Hung Hom station serves as the terminus of cross-border services with destinations to major cities in China including Beijing, Shanghai, Guangzhou, as well as Zhaoqing, Foshan, Dongguan in Guangdong. You can take Bus 11K, 11X, 21, 260A, 260X, 81C, 87D, N216, N241, N271 or N281 to reach the Hung Hom Station.
You can buy the tickets at Hung Hom or any Kowloon-Canton East Rail station. The tickets can be booked 60 days in advance. Passengers who is more than 10 years old need to buy the full fare tickets while the children between five to nine years old can buy the discount tickets. You can request a refund for an unused ticket at least two hours before the train’s departure. Need to mention that you must return the tickets to the same place where they were sold.
You can find more information on the MTR website http://www.mtr.com.hk/en/customer/services/cbs_introduction_tourist.html
You can also take the East Rail Line to Shenzhen as per instructions here and cross the border at Lo Wu and enter into Shenzhen at Louhu, or to Lok Ma Chau and enter Shenzhen at Futian.
In late 2018, the High Speed Hong Kong – Guangzhou – Shenzhen Rail link will open, more here