There's actually another way to get into this lovely country except taking flight.

Taking supply boat  (Nivaga III or Manu Folau) from Suva, Fiji.

It runs generally once a month or once every two months between Fiji and Funafuti.

However, boat schedule cannot be confirmed until around 2 days before departuring, and it takes about 3 days for one way trip.

There are different classes of cabin or stay on deck, and when book the ticket can also choose meal inculded or not. 

If going from Fiji, return ticket is required; however, refound is available if coming back by flight. 

If there's no time limited in Tuvalu and would like to see outter islands, follow the boat is the only and the best way to explore.

Supply boat would go outter islands after arriving Funafuti couple days later, and generally it would stay around half day on each island.

Therefore, there's enough time to hop on the island to explore, and hear some stories of each island during loading and unloading supplies, but make sure come back to the boat before baot leaving; otherwise, you would stuck on the island for a month or even longer.