Getting from Malaysia Kuala Lumper airport to Singapore by plane, train or bus is fairly straight forward.
Kuala Lumper to Singapore By Plane
By plane is easy, book plan, get to the airport and get on it;) The 2 airlines we used most was airasia.com and tiger airways and would recommend just going with the cheapest for your particular flight requirements.
Kuala Lumper to Singapore By Bus
Going by bus is the second quickest method after plane according to the people I spoke to in Kuala lumper airport with it taking about 4 hours. In order to get the bus need to get to the main bus station and the best way to do this is catch the klia train/metro and get of at stop “bandar tasik seletan”. Unfortunately the Klia doesn’t run directly from the airport but there is a shuttle bus just outside the airport! This is the purple coloured one and is in front of “the coffee bean”. The klia shuttle bus/train to bus station should be about 50rm or less. Then the bus to Singapore should be about 50rm(£12).
Kuala Lumper to Singapore By Train
Train is another option available and although it is slower there is sleeper trains which would allow you to get a bed or even a room so you can get some sleep on your way there. Catching this is basically same as the bus but you need to get to the train station which is the “KL Sentral” stop on the klia service. You will find a lot more information about getting the train in malaysia on this page, including pictures Of the various options available.