You need to know what you're doing when scuba diving. Or else you could have the minor inconvenience of serious injury or death.
For this reason, dive operators will not take you diving unless you show relevant certfication, i.e., that you have completed a training course with one of the certifying agencies, eg. PADI, NAUI, SSI, BSAC etc.
You can take the course with a dive school generally over a few weeks or you can do it more quickly if you are at a resort with a dive school which offers the course over a few days. The basic courses usually comprise a few theory lessons, swimming pool sessions and a few open-water sessions.
There are plenty of dive schools in Singapore so please use your fingers and google.
You have to be able to swim and be certified by a doctor as fit-to-dive. Other than that, diving in our warm tropical waters is not a particularly strenuous activity for someone of moderate physical fitness. And once you've mastered the basics, it is generally a stress free and relaxing activity.
Of course, the other major pre-requisites are $$$$$ and time. (Underwater photography requires even more $$$$$$.)
Good luck and Happy diving.