AZJUBILEE described the procedure correctly. I have done an international arrival once, but have been though HNL many other times.
The main terminal consists of three levels. The ground floor holds the baggage claim areas, located below the ticketing counters, as well as the airline club lounges, which are located in the center of the triangle that is at the base of the Central Concourse.
The second level is the main terminal level. The check-in counters and gate areas are here. When you arrive on a domestic flight, you come onto this level and, if you are in the Diamond Head or Ewa Concourses, go outside and can walk or board the Wiki Wiki.
International arrivals in Diamond Head and Ewa (not sure about Central) exit the jetway on the second level, but are immediately directed up to the third level, where passengers board a Wiki Wiki bus which takes them to customs and immigration.
One thing that is nice about Honolulu is that the Ewa and Diamond Head Concourses can be easily closed off, allowing easy international connections. When this is the case, international connecting passengers stay on the second level and can go to their connecting flight. I had a chance to observe this in 1999, when I took an Air Canada flight from Honolulu to Vancouver. I checked in at the main ticket counter, then went out to the Diamond Head Concourse. Right at the beginning of the Concourse, there were counters where my tickets were checked and I was allowed in. But once past I was not allowed to leave except on an airplane. This simplified things for later, when an Air New Zealand flight arrived and a lot of passengers came to the AC gate for my flight. Air Canada and Air New Zealand used HNL as a transit point for their Star Alliance service between AKL and YVR, and at the time, Oneworld (QF/CP) did the same.
Upon return to HNL, we were instructed that those, like me, who HNL was our final destination, were to exit the aircraft and go up to the third level and the Wiki Wiki bus, and those passengers continuing on NZ to AKL were to go into the boarding area.