Things you need to know beforehand

Weather
Singapore is located on the equatorial line, thus it is a tropical country. There are only two seasons there: rainy and summer. Rainy season runs from November to April, while summer starts in May and ends in October.

The temperature range from 23°C (73.4° F) to 31°C (87.8°F) [Wikipedia]. May/June is the hottest months of the year, while November/December is the coldest (no, there's no snow here). It is recommended to carry umbrella around, either to avoid the scorching sun in summer as well as the unexpected occasional rain in rainy season.
You can check the weather forecast for Singapore here.

Tips: As Singapore is an island, the weather is unpredictable. Don't fully trust weather forecast either, cos more often than not, the forecast is only for evening weather.

Languages
There are three main languages used in Singapore: English, Chinese Mandarin, and Malay. For formal announcements, Tamil (Indian language) is used as well.
An infamous language of its own kind in Singapore is the Singlish, or Singaporean English. It is a hybrid of Chinese dialect, Malay and English. Most foreigners have difficulty in understand this unique kind of English. Here are a few indications of Singlish (it'd take some time to understand them):

The past, the present, and the future are all the same.
Example: "Got time or not?" (Do you have); "This shop didn't have." (actually do not have).

Consist of words of it's own.
Examples: "She kena scold." (has been, being); "This rice is shiok." (delicious);

Special endings.
Examples: "What time, ah?"; "Don't be like that ler."; "That way lor."; "Over there lah!"

Singaporeans have their own accent too. This is the perfect example of that accent: Bolo Santosi.
For full lesson on Singlish, click here.

Currency
Singapore dollar, SGD or S$, is interchangeable with Brunei dollar.
The smallest value of coin is 5 cents and the biggest is $1; in between, there are 10 cents, 20 cents and 50 cents. For the notes, the smallest value is $2, followed by $5, $10, $50, $100, and the biggest is $1000.

There are many licensed money-changer across the island which offer a better exchange rate than most banks and hotels. You can immediately find money-changers in Changi Airport and Harbourfront. Click here for the complete list of money-changers
Use the converter on the right to see how much you'd need to change!

Visa
If you are from South-East Asia (Brunei, Cambodia, Indonesia, Laos, Malaysia, Myanmar, Papua New Guinea, Philippines, Thailand, Timor-Leste, Vietnam) you do NOT need a visa to enter Singapore.
Here are the list of countries that should have visa to enter Singapore: ICA.gov.sg

Telecommunications
Tourists don't usually need to buy a SIM card, as there are many public telephones available in the country. Every big shopping mall will have them for sure. However, in case you need a SIM card, you can find one in any 7-11 across Singapore.
Public phones can be found in almost every public places, like the malls and even on the streets. The phones are either coin or card operated. The cost is S$0.10 for 3 minutes. Phone cards can be purchased at 7-11, post offices, and small shop in the streets. Or, you can even use your own credit card at selected phone booths.
In many areas in Singapore, free wireless Internet and Wi-Fi called Wireless@Sg is available, but you'd need to sign up for a free account to use it.