The way to obtain authentication of a foreign public document is simple. For country or territory who has participated in Hague Convention abolishing the requirement of legalization for foreign public documents, it require a simple step.
You have to take the public document to the proper authority in that country and obtain a Certificate of Apostille certifying the signatures and/or seal of the issuing authority. In Hong Kong, the place doing such Apostille is The High Court of Hong Kong. You can do this by yourself or by instructing a local notary to do it on your behalf at a fee. But you have to check out what documents are qualified to do an Apostille: see Documents acceptable for apostille.
Here are the major nations being Hague Convention members: Australia, Belgium, France, Germany, Greece, Hong Kong, Hungary, Italy, Japan, Macau, Mexico, Netherlands, Norway, Portugal, Republic of Korea, South Africa, Spain, Sweden, Switzerland, United Kingdom of Great Britain and Northern Ireland and United States of America.