#1 recommendation for smooth pick up - make sure you and your vet get the paperwork 100% correct. There are so many ways to mess it up and a little error can result in a long delay at the cargo terminal or even quarantine. For example, my vet screwed up the date shots were given and expired (cathe form asked for one and he used the other). If the import agent hadn't caught it there before we flew and had the vet correct it quarantine would have resulted.
NelsonBlue's description of the self procedure pick up is great and very similar to my own experience. (However, still consider using an import export company for pick up... I have done a pick up and had an import-export company pick up different pets and would have to add that the expense (less than 500 HKD) for just picking up an animal is not much and makes the process much easier and faster. If there is any hold up the company can help resolve it. Also, you can accompany the agent in the cargo terminal if you want.)
But I have two notes for self pick up: (1) If you are going the pick it up yourself make sure to have HK dollars (cash) for the fees (They have card machines, but they seem to close them out after hours at the cargo terminal and (2) If at all possible, try to have a back up to help, in case you have an immigration hitch or other hold up at the airport, although quite unlikely (happened to a colleague and her dog ended up in quarantine after several hours waiting in cargo, and it was very difficult to retrieve).