There are not any direct flights from San Francisco to Belo Horizonte.
Belo Horizonte (BHZ) is located in the southeast region of Brazil and has an international airport (Confins) and a domestic airport (Pampulha). The shortest and most expensive route is flying American Airlines from SFO to BHZ with a stop in Miami. Rates are between $1200 - $1600 round trip depending on travel dates. You can also fly to São Paulo or Rio de Janeiro for around ~$1000 round trip, then to Belo Horizonte (40 min flight, ~$70 round trip).
American citizens need a tourist visa to enter to Brazil. Since January 25th, the process got a lot easier and now you can apply for it online and it will be ready in 72hrs max. The visa fee is 40$ plus taxes and its valid for 2 years. You can apply here http://www.vfsglobal.com/brazil-evisa/