Ms.HEALINGWINNIE,
There are three ways:

First, take direct trains from Guangzhou East to Hung Hom. It takes 1 hour and 45/55 minutes. Cost: HK$190. More details:
http://www.it3.mtr.com.hk/B2C/frmFareGuangdong.asp?strLang=Eng

Second: take direct bus. It takes around 3.5-4 hours and costs CNY80-100. Many hotels offers this service.

Third: take D trains from Guangzhou to Shenzhen. Then go through Luohu Boder to take HK mtr to HK downtown. The cost is more than direct bus but less than direct train.

Since you live at Chung King Mansion, I suggest you take direct trains. It is expensive. However, you can easily get to Chung King Mansion from Hung Hom.