Wellington is a really pedestrian friendly city and you can easily roam around the city on foot. However, buses are the most common and convenient way of commuting here. If you are a tourist, you can check with Metlink - (Greater Wellington Regional Council - Transport) at 0800 801 700, which provides all the information about the buses and their schedules. They also have a text bus service. You can text the bus stop number to the given contact, to receive the timings of the next bus which is scheduled to arrive at the same.
The diminutive capital city can also be best explored on foot like already said. The pathways are clean and dainty and friendly, and well suited for walking. Golden Mile is considered the backbone of the routes running from Railway Station down to Lambton Quay to the southern end at Willis Street. From here it runs further down to Manners Street, then to the Manners Mall, and then continues straight onto Courtenay Place. From the Manners Mall, there is an intersection for the Cuba Street and also to Te Aro. You can easily find a road map from several locations in town including the main visitor centre in Civic Square, the Central Library, and several convenient stores etc.