The cheapest way, short of walking or hitching a ride, to get between Singapore and Kuala Lumpur is by coach. Several companies ply this route so choosing which one to use is based largely on how convenient the departure and arrival points are to where you are, and where you want to go.
I used to use a company that departs from a shopping mall 10 minutes on foot from my office. My last trip with my usual bus company ended up taking 8 hours instead of 5. I did get to see a part of Singapore that I had never seen before and I took some photos while waiting for another bus to arrive so that the passengers could be consolidated. This is a smart move, business-wise, for the bus company but it made my normal trip intolerably long.
Unlike long flights on airplanes, there are no meals served, no movies to watch, and no toilets. That is why I changed bus companies. It is not as convenient for me to get to the new departure point (I have to take my luggage on the public transit) but at least once I am on the coach it is only 5 hours travelling time to Kuala Lumpur and a meal of nasi lemak and hot coffee were served on board.
Please note – there are sometimes long delays at the border crossings which are beyond the control of the bus companies.