The only practical way to reach Nanumanga is on one of Tuvalu's two government inter-island vessels, the Manu Folau or Nivaga III, sailing north from Funafuti. The schedule is irregular and depends heavily on weather and demand; expect roughly once a month, sometimes less in the cyclone season.
There is no air service. The reef passage on the west side of the island has no harbour — passengers and cargo are dinghy-shuttled through the coral, and the operation is sometimes called off in rough seas. Travel light, carry cash (no banks or ATMs), and plan to be on the island for at least as long as it takes the boat to return. There are no hotels; you stay with families, brought through arrangements made on the boat or by the island council.