Mangareva is one of the hardest places to reach in French Polynesia, and that is a large part of its appeal. Air Tahiti operates irregular flights from Papeete — the journey takes about three and a half hours, and flights run roughly once or twice a week depending on the season. Seats are limited and book up well in advance, so plan early. There is no regular ferry service from Tahiti, though cargo ships do make the passage occasionally; check with local operators if you want to travel by sea.
There is no paved road connecting the islands of the archipelago — inter-island travel is by boat, and local fishermen or small operators can arrange transfers between Mangareva and the surrounding smaller islands.