You'll need small change to buy an individual ticket. Alternatively, buy a special ticket deigned with tourist in mind. You gain entry to the trains by 'posting' your tickets into the barrier machine. After your trip, you 'post' your ticket into the barrier in order to leave. Escalators take you to the platform and train destinations are marked clearly.
Trains run frequently.
Do remember, eating and drinking are forbidden in MRT stations and trains. To simplify things for you, listed below is a handy list of stations close to various tourist attractions. All the outlying stations have taxi ranks nearby for extra convenience. Chinatown -10 minutes' walk down New Bridge Road, turn right into Smith Street. A recorded message played on the train will keep you on the right track.