Map from Google - Fernando_de_Noronha

The climate of the archipelago of Fernando de Noronha, near the northeast coast of Brazil, is tropical, hot all year round, with a dry season from August to January, and a rainy season from February to July. The archipelago is a UNESCO World Heritage Site.
Given the proximity to the Equator, the temperatures are stable throughout the year, and are slightly higher from November to April, when highs are around 30 °C, and slightly lower from May to October, when they are around 28/29 °C. At night, the temperature almost never drops below 20 °C.
Here are the average temperatures.
Average temperatures - Fernando de N.
Fernando de N.JanFebMarAprMayJunJulAugSepOctNovDec
Fernando de N.JFMAMJJASOND
Min (°C)252525242424242424242525
Max (°C)303030302929282829293030

In a typical year, about 1,400 millimetres of rain fall; the wettest months are March, April, May and June, when the rains are equal to or exceed 200 mm per month. Generally, the rainfall amount in February and July is acceptable, but in some years it may be more abundant, reaching the level of the rainiest months.
Here is the average precipitation.
Average precipitation - Fernando de N.
Fernando de N.JanFebMarAprMayJunJulAugSepOctNovDecYear
Fernando de N.JFMAMJJASONDY
Prec. (mm)6511026529028019012035201015201420
Days611171818131143123107

The driest period, in which it rarely rains, runs from September to December. October is historically the driest month, with fewer deviations from the norm, while in the other dry months, every once in awhile an intense shower may occur.
The rainfall distribution in Fernando de Noronha is similar to that of cities located in the north-east of Brazil, like Fortaleza and Natal.
Air humidity is high throughout the year, even in the dry season; however, fortunately sea breezes give a bit of relief.
The amount of sunshine is never scarce, because the rains come in the form of downpour or thunderstorm, and usually do not last long, however, the sunniest period is the dry season.

Sea in Fernando de Noronha

For swimming, the sea is warm all year round, as you can see in the following table.
Sea temperature - Fernando de N.
Fernando de N.JanFebMarAprMayJunJulAugSepOctNovDec
Fernando de N.JFMAMJJASOND
Sea (°C)282828292828272727272727

When to go

The best time to visit the archipelago of Fernando de Noronha, to explore the islands on foot, or for sunbathing, swimming and diving, goes from August to January, being the driest of the year. Surfers will appreciate especially the period beginning in November and peaking in February and March, when waves are higher.