Map from Google - Puerto_Rico

The climate of Puerto Rico is tropical, hot all year round, with a rainy season and a relatively dry season from November to March, which however, does not occur everywhere. The north-east trade winds, which blow in the cool season, from November to March, discharge the humidity, which has been picked up in the sea, in the form of rain, especially on the northern side, which therefore is rainier than the southern side. For example, in San Juan, 1,400 millimetres (55 inches) of rain per year fall, including more than 100 mm (4 in) per month between May and December, while the driest months, in which about 55 mm (2.2 in) of rain per month fall, are February and March, that is, at the end of the period of the trade winds, when they become weaker.
Here is the average precipitation in the capital San Juan.
Average precipitation - San Juan
San JuanJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)805060901451201251501501501401151375

The rainiest area is the interior, in particular the north slopes of the Cordillera Central, and even more those of the Caribbean National Forest (or El Yunque), where there is no real dry season. On Pico del Este, about 1,000 metres (3,300 feet) above sea level, 4,300 mm (170 in) of rain per year fall.
In contrast, along the southern coast, sheltered from the trade winds, the rainfall often drops below 1,000 mm (40 in) per year, and the winter is particularly dry, as happens in Ponce and La Parquera. On the south coast, there is also a certain break in rainfall in June and July.
Here is the average precipitation in Ponce.
Average precipitation - Ponce
Prec. (mm)252540559565651101501609535915

Isla Mona, to the west, is almost dry, while the island of Vieques, to the east, is a bit rainier, since the annual rainfall amounts to 1,070 mm (42 in) per year.
There is also a difference in climate between the western and the eastern coast of Puerto Rico: the rainy season is slightly longer on the east coast, where it lasts until January included, while on the west coast it lasts until November or mid-December.
Anyway, the rains in Puerto Rico occur mainly in the form of showers and thunderstorms, usually not long-lasting, therefore the amount of sunshine is always acceptable: in San Juan it ranges from 7 hours a day in the period November-January, to 8 hours a day in rest of the year.
Anyway, from June to November, the archipelago can be hit by tropical storms and hurricanes, which are most likely between August and October.
As mentioned, the temperature is high all over the year, however it's slightly higher in the period from May to October: highs are around 32 °C (90 °F) in summer, while they are around 27/29 °C (81/84 °F) in winter. In addition, in the hotter period high humidity makes the heat uncomfortable.
Here are the average temperatures of San Juan.
Average temperatures - San Juan
San JuanJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)222223242525262625252423
Max (°C)282929303132323232313029
Min (°F)727273757777797977777573
Max (°F)828484868890909090888684

At higher altitudes, the temperature is slightly lower: for example, in Adjuntas, at 500 metres (1,600 feet) above sea level, highs range from 25 °C (77 °F) in winter to 29 °C (77 to 84 °F) in summer, while on Cerro Maravilla, the fourth highest peak on the island, at 1,200 metres (3,900 feet), highs range from 20 °C in winter to 22 °C (68 to 72 °F) in summer.
Every now and then, from December to March, the archipelago can be affected by cool winds from the United States, which can lower the temperature by a few degrees, although in a less noticeable way than in Cuba and Yucatan (Mexico), which are closer to the American continent.

Puerto Rico

The sea is warm enough for swimming all year round: the water temperature ranges from 26 °C (79 °F) from January to March, to 29 °C (84 °F) from August to October.
Sea temperature - San Juan
San JuanJanFebMarAprMayJunJulAugSepOctNovDec
Sea (°C)262626272728282929292827
Sea (°F)797979818182828484848281

When to go

In general, the coolest and least rainy period in Puerto Rico runs from December to March, which is also outside of the hurricane season; more in particular, we can find the best time depending on area: February and March along the north and east coasts, from December to March along the south and west coast, because they are generally the least rainy periods. In April there is a certain increase in rainfall, especially in inland areas.
In summer, the heat is sweltering and showers are frequent, in addition, there is a certain risk of tropical storms and hurricanes. If you want to visit Puerto Rico in summer, you may prefer the south coast, which is less rainy, especially in June and July, when there is a certain decrease in precipitation.
The Americans have introduced the habit of using air conditioning, so inside buildings there are often much lower temperatures than outside, so it can be useful to bring some warmer articles of clothing, at least for those who are sensitive to cold.

What to pack

From December to April: light clothes, a sweatshirt for the evening.
From May to November: tropics-friendly, lightweight clothing, possibly a light sweatshirt and a light raincoat for thunderstorms; a light sweatshirt and pashmina for airconditioned places.