Most people arrive in Singapore by air. Its status as a major airline hub in Asia makes Singapore a natural starting or ending point for a multi-country tour of Southeast Asia. Since its an island, you can naturally arrive by sea, although it seems that very few do. Lastly, you can get to Singapore by road or train from Malaysia.
As noted above, Singapore is a major air hub. Most large international airlines have routes to Singapore, in addition to the island's own highly regarded airline, Singapore Airlines.
A number of regional airlines, especially budget carriers, call on Singapore, and a few of them are even based there. Here's a short list:
Changi rates high on many people's lists of the world's best airports. It certainly rates high on our list as well. The shopping and food outlets on offer are extensive and various, although the prices aren't that much of a bargain. Add to that free Wi-Fi and plentiful free internet terminals as well as day rooms, complete gyms and easy access to the city.
Singapore can be reached by train from cities in peninsular Malaysia or Thailand. Malaysian Rail has daily trains traveling up and down the entire length of the Malay peninsula.
Traveling by bus is not something that readily comes to mind, but there are some excellent services between Singapore and Malaysia that offer a level of comfort that can even out-do first class air flight. Check out Plus Liner or Konsortium for more information.
Citizens of the USA, EU and Commonwealth countries do not require a visa to enter Singapore. These travelers will receive a minimum of 14 days' visa free entry. US citizens get as much as 90 days, depending on the form of entry.