Map from Google - Palau

The climate in the archipelago of Palau (or Belau) is equatorial, that is hot, humid and rainy throughout the year. In fact there is not a real dry season, but only a relative decrease in the frequency of showers and thunderstorms between February and April. The rains are plentiful and amount to around 140 inches per year; the rainiest months are those of summer (June, July and August), even though we cannot speak properly of summer, because the temperature is stable throughout the year.
Here is the average precipitation in Airai airport.
Average precipitation - Airai
AiraiJanFebMarAprMayJunJulAugSepOctNovDecYear
AiraiJFMAMJJASONDY
Prec. (in)117.97.58.712.215.616.71512.413.210.611.8142.5
Days201717161718191917191820217

The amount of sunshine is acceptable from January to May, and lessens a bit from June to December, when the showers occur almost daily, though a little sunshine is almost always present, except when the typhoons, ie the tropical cyclones of south-east Asia, pass over the country (then, they make their way to the Philippines). Typhoons, along with the less intense tropical storms, bring rains and strong winds and occur between June and November. The southernmost atolls, like Sonsorol and Hatohobei, being near the equator, are protected from typhoons.
In the capital Ngerulmud (or Melekeok), the daytime temperature is around 86/88 °F all year round, while at night it's around 73/75 °F.
Here are the average temperatures of Palau.
Average temperatures - Ngerulmud
NgerulmudJanFebMarAprMayJunJulAugSepOctNovDec
NgerulmudJFMAMJJASOND
Min (°F)737373757575757575757575
Max (°F)868686888888868686888888


Palau

For swimming, the sea is warm all year round, and has a very stable temperature, as we can see in the following table.
Sea temperature - Ngerulmud
NgerulmudJanFebMarAprMayJunJulAugSepOctNovDec
NgerulmudJFMAMJJASOND
Sea (°F)828282848484848484848484

When to go

The best time to visit Palau runs from February to April, being the driest and sunniest. Even in this period, however, showers and thunderstorms must be put into account, but they soon give way to the sun.

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.
For the reef, equipment for snorkeling, water shoes or rubber soled shoes.