If you plan on using city buses a lot, it's worth buying a Smartlink Travel Card (available from the Metro kiosk, the Visit Belfast Welcome Centre and the Europa and Laganside bus stations). The card costs an initial fee of £1.50, plus £10.50 per 10 journeys – you can get it topped up as you want. Or you can get seven days of unlimited travel for £16. When you board the bus, you simply place the card on top of the ticket machine and it automatically issues a ticket.
The Belfast Visitor Pass (per one/two/three days £6.50/11/14.50) allows unlimited travel on bus and train services in Belfast and around, and discounts on admission to Titanic Belfast and other attractions. You can buy it at airports, main train and bus stations, the Metro kiosk on Donegall Sq and the Visit Belfast Welcome Centre.