The best way to begin learning Cantonese or Mandarin will be to take regular classes with professional instructors. There are numerous opportunities to find formal instruction in Cantonese and Mandarin, notably in Hong Kong´s universities, most of which offer language classes. Some of these are even open to the general public.
One popular language school is the Hong Kong Language Learning Centre, which offers instruction in both Cantonese and Mandarin for adults (sixteen years or older). The Centre offers different levels of instruction from beginning to advanced. It also offers conversation classes to help you improve your fluency in speaking. Classes are designed to immerse students in a Chinese environment, which increases learning speed and retention. You can also choose to take courses centred on business vocabulary and interaction if you are learning the language for work.
Chinese language exchange
Once you have learned some basic skills and vocabulary, you may want to consider a language exchange (or tandem pairing) with a native Mandarin or Cantonese speaker. This will allow the two of you to meet and practice your language skills. Language exchanges can be done either formally through organized programmes (especially common at universities) or on an informal basis. Language exchange and tandem language pairings are two of the best ways to practice and learn a foreign language, since they allow you to learn practical grammar, pronunciation, vocabulary and even some culture in a relatively informal setting.
Dictionaries and phrase-books
Whether you decide to learn Cantonese and Mandarin in their entirety or not, you will at least want to arrive in Hong Kong with a pocket dictionary. This way you will have a resource you can use in daily situations: at the grocery store, for reading signs, or even getting directions.
Most dictionaries and phrase-books will also contain common questions, answers, and even slang that you will need to use during day-to-day life. This is a great way to put a lot of vocabulary at your fingertips, but it is not nearly as effective as formal instruction or a language exchange.
A final and very efficient method for improving your language skills is to immerse yourself in the language as much as possible. Watch Cantonese or Mandarin language films and listen to radio broadcasts in either language, even if you cannot completely understand them. When you´re in Hong Kong, interact with locals and use the language as much as possible, reverting to your native language or English only when absolutely necessary. This kind of immersion will help you develop an ear for Cantonese or Mandarin, and get you thinking in those languages as well.