Brasília was built for cars, and you will need either a car, a ride-share app, or a lot of patience for the bus system. Distances are deceptive — what looks close on the map can be a long walk in 35°C heat with little shade and few pedestrian crossings. Uber and 99 work reliably and are reasonably cheap.
A small metro runs between the central station and the southwest suburbs but is not useful for sightseeing. The cheap and frequent Rodoviária do Plano Piloto is the city's main bus hub, just below the platform between the two axes. For the monumental axis itself, several bus circuits start from there — buses 108 and 131 cover the main sights.
If you visit on a Sunday, the Eixo Monumental is partially closed to cars and turns into a long urban park — perfect for cycling end-to-end.