Map from Google - Singapore

The climate in Singapore is equatorial, ie hot, humid and rainy, throughout the year. The country, which is at the same time an island, a city and a state, is actually at the Equator, in an area where there is always the opportunity for the formation of showers and thunderstorms.
Although the climate is fairly uniform, you may notice some changes in the course of the year, due to the two monsoons: the one from the north-east, occurring from November to early March, is more rainy especially in the first part, and the one from the south-west, occurring from June to September. The first period between the two monsoon, from March to early June, is the hottest and the most unpleasant of the year.
Throughout the year, about 2,400 millimetres (94.5 inches) of rain fall, with a peak of around 250 mm (10 in) per month in November, December and January, while in the rest of the year, from 150 to 200 mm (6 to 8 in) per month fall, so there is no month without abundant rainfall. From November to January, the rains in addition to being more abundant, are more frequent and last longer, and usually occur in the afternoon or in the evening. On the other hand, that of the south-west monsoon is the period of the so-called Sumatra squalls, occasional thunderstorms accompanied by wind gusts, occurring in the hours before dawn or in the morning, and caused by a squall line coming from the island of Sumatra; otherwise, in this period there can be short thunderstorms in the afternoon. In addition to thunderstorms, during the period of the south-west monsoon, from the island of Sumatra, even clouds of smoke and haze caused by forest fires may come, which in the worst occasions can create a pall of unhealthy air, which can be dangerous for the population. In general, this can happen until mid-October.
In the city there are many covered footpaths and walkways, made to protect passers-by from the rain.
Here is the average precipitation.
Average precipitation - Singapore
SingaporeJanFebMarAprMayJunJulAugSepOctNovDecYear
SingaporeJFMAMJJASONDY
Prec. (mm)2501752001951751701651901802102502652425
Prec.(in)9.86.97.97.76.96.76.57.57.18.39.810.495.5
Days171213151513131514161919181

Temperatures in Singapore are quite uniform, since they vary only by a few degrees between the cooler and the warmer months. The minimum temperature goes from 23 °C (73 °F) in December and January, to 25 °C (77 °F) in May and June, while the maximum ranges from 30 °C (86 °F) in December and January to 32 °C (90 °F) in April and May. Even the records are close to the averages: at night, temperatures almost never reach 20 °C (68 °F), while during the day they rarely rise above 33/34 °C (91/93 °F). But it is especially the constant humidity that makes the weather annoying, since the relative humidity doesn't often go below 70%, even during the warmest hours. If you add to this the urban heat island effect, typical of big cities, where the heat is trapped between streets and buildings still at night, you will understand how the climate of Singapore is not very pleasant for those who are not used to it. The sea breezes can relieve a little the feeling of heat in the harbor area and in the neighbourhoods along the coast, while apart from the breezes, there can be some wind only in January, February and March, ie in the second part of the northeast monsoon. For the rest, heat and flat calm dominate, at least within the city. Fortunately, buildings and means of transportation are equipped with air conditioning.
Here are the average temperatures.
Average temperatures - Singapore
SingaporeJanFebMarAprMayJunJulAugSepOctNovDec
SingaporeJFMAMJJASOND
Min (°C)232424242525242424242423
Max (°C)303131323231313131313130
Min (°F)737575757777757575757573
Max (°F)868888909088888888888886

The amount of sunshine is never very good, since there's an average of 5 or 6 hours of sunshine per day for most of the year; we remind that at the equator the day lasts 12 hours throughout the year. The least sunny months are November and December, with 4 hours of sunshine per day, while February is the sunniest, with 7 hours. However, the equatorial sun is very strong, so you have to be careful even on cloudy days.

Singapore

Singapore is not exactly a destination for beach tourism, however, the sea is warm all year round.
Sea temperature - Singapore
SingaporeJanFebMarAprMayJunJulAugSepOctNovDec
SingaporeJFMAMJJASOND
Sea (°C)282828293030292929292928
Sea (°F)828282848686848484848482

When to go

Although there is no big difference between the periods, probably the best month to visit Singapore is February: it's the sunniest, and on average there are "only" 12 days of rain. November and December are among the cooler months, but they are also the wettest: it rains almost every day, and sometimes the rain lasts more than in the other seasons. January and February, in the second part of the "winter" monsoon, are less rainy, and in any case they are not as muggy as March, April and May, also because they are the only months in which there's a bit of wind. After the hot period from March to early June, July and August are also fine, if you can only go in this period: all in all the difference with January and February is small.

What to pack

All year round: tropics-friendly, loose fitting clothing, a scarf for the breeze, light sweatshirt and pashmina for airconditioned places, light raincoat or umbrella.
For the reef, equipment for snorkeling, water shoes or rubber soled shoes.