Book the cheapest tickets at least 1 month before departure directly on the company's website www.hawaiianairlines.com or on general search engines. You will almost certainly use Hawaiian Airlines at least once when visiting the Hawaiian Islands, where they operate a very dense and frequent inter-island network (often several times per hour), with many direct flights to the mainland USA, Australia or Japan.
If you plan to fly between the Hawaiian Islands, you may prefer Sotuhwest Airlines, which flies at similar prices but with two free checked bags.