Probably the cheapest way to get to Singapore depending upon where you are coming from would be by airplane. You can get cheap flights around the world if you are not committed to a certain time of the year. As a matter of fact, you can really plan a cheap vacation if you plan in advance and plan smartly.
A Singapore trip can be the same. If you are wanting to plan a cheap trip once you get to Singapore, you have to also plan in advance. You also have to be willing to miss seeing certain things. This is because you can go to a main place that has many things to do nearby. Then you can walk to the places. Walking is free and you can go to many places.