Your hotel can usually arrange transfers to and from the airport. This is usually a per person rate and can sometimes be quite high.
You may be able to hire a car from the airport. Please note that roads in Fiji have poor lighting, have only one lane most of the time, and are sometimes in a state of disrepair.
Fiji has cheap local buses and cheap air conditioned long distance coaches that can be caught at the airport and along most bus stops along the Kings and Queens road. As a guide from the airport to Sigatoka should be around $10 FJD per person or less. They are frequent but not always on time and stop running from the airport early evening. Yellow buses run from Nadi Town to Denarau for $1.
Its fun catching a mini bus as you will meet many of the friendly locals. These can be hailed from bus stops and are similar prices to the coaches. They often have their route painted on the outside of the mini bus. Always best to have small change when using these. As a guide Nadi to Suva is usually around $18 FJD.
When using taxis always get an estimate before you get in and make sure it has a meter as some taxis are not regulated.
Fiji has a very organised hitching system. Only for the adventurous and this is usually the only way we like to get around. Whilst at a bus stop you will often see a car flash their lights. This means they will take you in your direction for a small payment starting at $3FJD. Fijians are very social people and will take delight in meeting you. A fun way to travel, but do so at your own risk.