Honolulu, Oahu and Kahalui, Maui are serviced by a large number of international and domestic airlines. To fly between the islands most people use Hawaiian Airlines. There are smaller airlines which can be fun for flying between the islands. These are Mokulele Airlines and Island Air.
Each island has a great bus system. If you are on Oahu you can take The Bus. (Checkout their mobile app). When on the Big Island you can use the Hele-on bus. Find the Maui Bus schedule online. The Garden Isle, Kauai Bus can be used to get around the island.
Most car rental agencies have rental desks in or around the airports at each island.
Taxis and Uber
Each island has taxis. The number to know on Oahu is 222-2222. It's easy to remember when you know that tutu means grandmother!
Uber has limited availability in the islands. It's best to check the Uber app for availability before traveling.