reservations (see link) are a must. Tours are given from Wednesday through Saturday at 8:30 am, 11:30 am, and 1:30 pm and take about 1-1/2 hours. You meet at the Honolulu Academy of Arts and take a shuttle to the house.
If you don't want to wait, you can also take the virtual tour, but you miss out on the sights like the small harbor built for Doris Duke's yacht.
Doris Duke was the wealthy heiress of the late tobacco and hydro-electric energy magnate, James Buchanan Duke. Duke and his colleagues started the Duke Power Company, which eventually became part of Duke Energy. She inherited her fortune upon the early death of her father at the age of 12, but was not involved in any of her father's businesses. As a socialite, she later met and married James Cromwell. They traveled the world on their honeymoon, stopping by the Middle East, India, and Hawaii. They enjoyed their stay in Hawaii so much they extended their honeymoon by 4 months. During that time, Doris Duke and James Cromwell purchased 5 acres of beach front property and commissioned construction of what is now Shangri-La.