As publishers of guidebooks, we have taken nearly 100 flights to and around the Islands, and all but 5 or 6 were as passengers of Hawaiian Airlines. We've learned to go with the Hawaii specialists. Their hospitality gets the vacation started once you fasten the seatbelt. BTW: We have no deals or partnerships or any reason to tout this carrier.
Some flights from major West Coast Airports fly direct to the outer islands, like Maui. But most flights go through Honolulu (Oahu) and you have to transfer across the airport to catch an inter island flight.
At the main terminal in Honolulu a free shuttle bus (the Wiki Wiki) makes the five-minute journey to the smaller terminal. Or, if you have time to spare, load the carryons and walk (your bags will be checked through to the outer island).
In the post war romantic period of the Islands, ocean liners brought most visitors. Hawaiian Air today is the closest you're going to get to vintage tourism.
More often than not, you will get a good eyeful of Waikiki coming into Oahu (from the south in this shot). Flights that approach from the north go over the USS Arizona Memorial at Pearl Harbor.
To keep the aloha spirt alive once in Hawaii, check out the Trailblazer guides to all-things-outdoors, plus all the cultural sites and tourist attractions. The visitor safety sections in the Trailblazers are a good enough reason to bring one along—possibly a life saver.