The Yui Rail monorail runs from Naha Airport through the city centre to Shuri, with 19 stations. It covers the main attractions (Kokusai Street, Tsuboya, Shuri Castle) and runs frequently. A one-day pass is good value if you are making multiple trips.
Beyond the monorail, you will need a taxi or bus. Taxis are metered, reasonably priced by Japanese standards, and drivers are professional. City buses cover the wider urban area but routes can be confusing for non-Japanese speakers. For exploring anywhere beyond central Naha — the northern parts of Okinawa Island, the beaches, the US military sites — you will need a rental car, and international driving licences are accepted.