Funafuti International Airport is the only point of entry into Tuvalu. Fiji Airways operates the only scheduled commercial connection, with a small turboprop from Suva (about three hours' flight time). Frequencies are limited — typically two or three flights a week — and the schedule changes seasonally, so book well in advance and build slack into your dates: cancellations and delays for weather are common.
The other practical option for the seriously patient is by sea: the inter-island vessels Manu Folau and Nivaga III work the outer atolls from Funafuti, and the country's small port occasionally receives supply ships from Fiji that will carry passengers if you ask in advance. There is no scheduled passenger ferry from anywhere else, and no other airline serves the country at present.