You can get detailed information at the Hawaii forum, but when deplaning the Hawaiian Air flight, follow the signs that will lead you to the WikiWiki shuttle that runs between terminals - if you exit security and take the wrong route, you can take the shuttle outside, but it will take alot longer and you will need to clear security again...make sure you follow the correct signs. The same is true for your inbound HNL flight - take the same shuttle to the interisland terminal to avoid clearing security there (you can check-in for HI once inside the terminal)

If you have any questions, ask a Hawaiian Air rep when deplaning your interisland flight to be directed to the terminal shuttle (or your mainland flight upon arriving)

If you have bags to claim at either point, you will need to exit the secure area and go to baggage claim, take the outdoor WikiWiki shuttle, and reclear security - so try to either avoid checking bags, or get them checked through to your final destination.

You will still need to clear the Agricultural Inspection, where your bags are X-Rayed for prohibited food/fruit - this checkpoint is right in front of the shuttle boarding lounge - and don't try to sneak any fruit, they're very good at finding it, even the small passionfruits we picked at the side of the road and planned to enjoy inflight