The nearest airport is Confins (CNF) at Belo Horizonte, about 130 km away. From the airport, the cheapest route is the airport bus to Belo Horizonte's main bus station, then a Pássaro Verde coach to Ouro Preto (about two hours, departures every hour or so). Total time, airport to Ouro Preto, is around four hours. Private transfers cut this to roughly two and a half hours but cost about ten times as much.
From other Brazilian cities, the long-distance coach is the standard option. Belo Horizonte is the main hub: buses also run direct from Rio de Janeiro (about seven hours overnight). The bus station in Ouro Preto is a steep ten-minute walk from Praça Tiradentes, or a short taxi ride.
There is no train service into Ouro Preto. The historic Maria Fumaça steam train still runs between Ouro Preto and the nearby town of Mariana — but as a tourist excursion, not a means of getting in or out of town.