Map from Google - Tuvalu

Tuvalu (formerly Ellice Islands), an archipelago located in the Pacific Ocean, south of the equator, has an equatorial climate, ie hot, humid and rainy throughout the year. The rains, occurring in the form of downpours of thunderstorms, can be intense, but usually do not last long, and do not greatly reduce the hours of sunshine.
Temperatures are very stable, around 25 °C (77 °F) at night, and 31 °C (88 °F) during the day. The trade winds blow all year round, but especially in the period from April to October, tempering a little the heat.
Here are the average temperatures of the capital Funafuti.
Average temperatures - Funafuti
FunafutiJanFebMarAprMayJunJulAugSepOctNovDec
FunafutiJFMAMJJASOND
Min (°C)252525252525252525252525
Max (°C)313131313131313131313131
Min (°F)777777777777777777777777
Max (°F)888888888888888888888888

Precipitation is definitely abundant, since it exceeds 3,000 millimetres (120 inches) per year.
In the capital Funafuti, 3,200 mm (126 in) of rain per year fall, with a peak between December and March, when rainfall is equal to or greater than 300 mm (12 in) per month, and a minimum (very relative...) between May and October, when it drops below 250 mm (10 in) per month. Here is the average precipitation.
Average precipitation - Funafuti
FunafutiJanFebMarAprMayJunJulAugSepOctNovDecYear
FunafutiJFMAMJJASONDY
Prec. (mm)3603153152502352052352302002402753353190
Prec.(in)14.212.412.49.89.38.19.39.17.99.410.813.2125.6
Days181820191919202019191817226

In the northernmost islands, the rainfall is slightly less abundant.
The Tuvalu islands are affected by tropical cyclones of the Southern Hemisphere, in the period from November to mid-May (although sometimes they have occurred outside of this period, as happened with Bebe on late October 1972, and Keli in June 1997). Being not far from the equator, the islands are generally affected by cyclones at the beginning of their formation, but considering that Tuvalu is one of the flattest countries in the world, cyclones can cause flooding, but also storm surges, even if they are not are very strong or if they pass at a certain distance. The northernmost islands (Nanumea, Niutao, Nanumanga), closer to the equator, are located at the edge of the area, where cyclones are rare.

Funafuti

For swimming, the sea in Tuvalu is warm all year round, as we can see in the following table.
Sea temperature - Funafuti
FunafutiJanFebMarAprMayJunJulAugSepOctNovDec
FunafutiJFMAMJJASOND
Sea (°C)292929303029292929293030
Sea (°F)848484868684848484848686


When to go

The best time to travel to Tuvalu goes from mid-May to late October, being a relatively less rainy period, and out of the cyclone season. Since sometimes there have been cyclones outside of the canonical period, to go on the safe side, you can choose the period from July to mid-October.

What to pack

All year round, tropics-friendly, loose fitting clothing, sun hat, a scarf for the breeze, a light sweatshirt for the evening, light raincoat or umbrella.