There is a departure tax of NZ$55 per person adult and $15 per child between 2 and 12. It is only payable in cash. No tax is payable for children under 2.
By plane
Rarotonga International Airport IATA: RAR is the main gateway to the Cook Islands. There are daily services to Auckland 3.5 hours and weekly services to Sydney, Fiji and to Los Angeles. The only international airlines at present are Air New Zealand and twice-weekly Pacific Blue. Air New Zealand has code share arrangements with other Star Alliance members including United Airlines and Rarotonga is a popular stopover on Round the world flights.
See the Rarotonga article for airport details.
By ship
Rarotonga and Aitutaki are regular stops for cruises operating from Tahiti. Other cruise companies also stop by occasionally.
If you're planning to sail to the islands you must enter through one of the five designated ports of entry. These are Rarotonga, Aitutaki and Atiu in the Southern group, and Penrhyn and Pukapuka in the Northern group.