Most airlines fly into Singapore's heavily trafficked Changi International Airport. The best way to get from the airport to the city(20km/12mi away) is by train, but there is also a wide choice of bus and taxi services.
Singapore is the southern terminus of Malaysia's rail system, and three trains go to Kuala Lumpur each day. If you're going to or coming from Malaysia, you have several options, ranging from comfortable buses to taxis.