When getting around Singapore, the MRT (mass rapid transit) system is probably the fastest way to get from one point to the other.
Just get an EZ-Link stored-value card or a Singapore Tourist Pass at the Airport train station when you arrive.
This will allow you unlimited travel for one day (S$10), two days (S$16) or three days (S$20) on trains and basic bus services.
Use CityMapper app to making planning journeys on Singapore's public transport much easier, by allowing you to check nearby departures in real-time, find the fastest route with various transport options, and alert you in cases of train faults. Google Maps works pretty well in Singapore also.
Alternatively, you may choose to use a service like Grab, which allows you to book private taxis/drivers, or share a ride with others.