If you're not bringing in forbidden items, your arrival experience in Hawaii (when flying in from the U.S. Mainland) is no different than at other U.S. airports when arriving on a domestic flight. You go to baggage claim, take your bags, and proceed to your shuttle, taxi, or rental car. There's nothing that's similar to a U.S. Customs and Immigration clearance.
If, when filling out the Agricultural Declaration Form, you discover that you have something you shouldn't have (such as live plants) in your checked or carry-on bags, you take these items to the Hawaii Department of Agriculture in the arrival area (or discard them in an amnesty bin).
On departure from Hawaii back to the mainland, there's one extra step. Before you check your bags with your airline, your bags need to go through a U. S. Department of Agriculture x-ray conveyor belt and have stickers applied.