Singapore has one of the most extensive and efficient public transportation systems in the world.  Travelling in the city and suburbs is typically a quick and affordable affair. 

The Mass Rapid Transit (MRT) operates a network of trains serving 51 stations.  Trains operate from 5.30am -12.30am daily, every three to eight minutes.  A ride on the MRT from Singapore Changi Airport to the city takes less than half an hour.
Public buses run daily from 5.30am - midnight.  Extended night services cost slightly more. 

The fare collection system is based on contactless cards called EZ-link card and fare boxes to pay cash on board buses.
Rides on the MRT cost from 80 cents to S$1.80 and you must have a contacless card to enter the system. If you do not have an EZ-link card you can purchase a contactless ticket on a ticket vending machine. After use, you can get your 1$ deposit back from any vending machine by re-introducing your ticket in the machine. 
The EZ-link card is a stored-value card giving discounted fare for multiple rides, the fare depends on the number of zones travelled.  The EZ-link card may be purchased and topped up at most MRT stations and bus interchanges.