No official website for booking trains ticket run by the China Railway Administration. So, if you want to book one, you should handle through a ticket agent. You can book the train from TravelChinaGuide. If you want to see these three cities, it should be go Hong Kong to Shanghai, Shanghai to Beijing. Hong Kong side offer booking on line and you can find information on MTR official website.

Thank you very much Liz, for replying my queries.
What is the the best railway root, and train nos for the following:
Hong Kong to Shanghai

Thanks & Regards,

Ravinder

Dear Liz,

Thanks for your reply.
In case, in future you want any travel information/guidance how to reach & Travel indian cities (Delhi, Mumbai, Bangalore, Kolkata, Chennai, Hyderabad, Agra, Jaipur, Jodhpur, Kashmir etc, by rail, plane or bus, website for booking tkts etc, pl do write me. It will be my pleasure to answer you. You can write me at rediffmail.com|ravinderjalali.
Thanks & With regards,
Ravinder Kumar Jalali

There is only one train from Hong Kong to Shanghai: T100. One train every two days.
Thank you, Mr Ravinder. I will. Have fun in China.

Dear Liz,
You are right, T 100 train is from Hong Kong to Shanghai and I believe T 99 train is from Shanghai to Hong Kong. My Colleague has the meeting in Shanghai. We have decided the following root for him, Delhi-Hong kong-Delhi by Plane & Hongkong-Shanghai-Hong Kong by Train. In fact there are direct flights from Delhi to Shanghai, but we want to travel by trains also, since we have heard rich experiences about Chinese trains.
Dear Liz, you will agree that Indian Railways in India too are most economical, convenient, cheaper, safer & faster transportation in India.
I will keep you posted. Thanks.