Fiji Airways operates flights from Nadi and Suva to Savusavu Airport (SVU), the island's main airfield. The flight from Nadi takes about an hour; from Suva about 30 minutes. Labasa also has a small airport (LBS) with connections to Suva.
The alternative is the ferry from Natovi Landing (near Suva on Viti Levu) to Savusavu, operated by Goundar Shipping. The crossing takes around 10–12 hours overnight, arriving in Savusavu in the morning. It is cheap and practical if you don't mind the night passage. Seats and simple cabins are available. The ferry also connects Savusavu to Taveuni.