No pre-arranged visa is required to visit the Cooks, as long as you're here on holiday. A visitor permit, good for 31 days, is granted on arrival for all nationalities. The only things you need to do are present a valid passport, an onward or return airline ticket, and honour the loosely policed 'prior booking' arrangement.
If you want to stay longer than the initial 31 days, you should have no problems as long as you can show you've got adequate finances and still have your vital onward or return air ticket. Extensions cost NZ$70/120 for up to three/six months.
Visitor permits can be extended on Rarotonga at the Ministry of Foreign Affairs & Immigration office (29347; firstname.lastname@example.org; PO Box 105, Avarua, Rarotonga), on the top floor of the government building (the big three-storey white building behind the Banana Court in Avarua). Come in a week before your current visitor permit expires.
If you want to stay more than six months, you must apply in advance from outside the country to the Ministry of Foreign Affairs & Immigration. If you are intending to visit the outer islands you'd be wise to extend your permit beforehand, as there are often delays.