Read HRS134, each section.
Like Justin posted here's a small breakdown.
All firearms must be registered with HPD (Honolulu Police Department) at their main station within 5 days of landing. However, due to COVID-19, they are not taking walk ins anymore. You must make a reservation online.
https://app.acuityscheduling.com/schedule.php?owner=19367924 CLick on registration of firearms and then out of state. There was a proclamation that waived the 5 days to register due to COVID, so you do it as soon as you can. Many have been trying for months to get an appointment. So biggie since it was waived. During this process, you must take each firearm to HPD and show it to them. There is no online way to register. They may measure your rifle barrels so make sure none are below 16 inches and 18 inches for shotguns.
HI has a strict "to and from law" you can only transport firearms from your residence to the range, police station, gun store, gun smith, place of business. So no grabbing coffee or lunch on the way to the range or on the way back home. You cannot even pick up a friend with a firearm in the car. HI treats ammo and firearms the same. So even if buying ammo at a store, you cannot go and grab a coffee after. You must go home or to the range or to work.
No pistol mags over 10rds, rifle are OK for now. They are trying to ban those right now SB301 this legislative session.
HI does not issue CCW or open carry permits, and shares no reciprocity with other states. This also applies to ammo. Cannot keep ammo on yourself in public without one of these permits. So don't forget to empty your range bag if using not for the range and pockets if going somewhere after the range.
If you decide to buy a firearm in HI, you must apply at HPD and they will do a mental health check as well. So if you saw any type of mental health provider, then they will have to sign a waiver that you're OK. You also need to make an appt in the link above to apply for a "permit to acquire". But good luck, people have been trying for months to get an appointment.