Foreign participants should plan to arrive GRU or Viracopos Airport (in Campinas city).
São Paulo Bus/Coach Station is called Terminal Tietê.
Option 1: Take the Airport Bus Service (https://www.airportbusservice.com.br) to Terminal Tietê. There is a bus every 50 minutes and the cost is about R$ 40. The journey will take between 25min and 2h (depending on the traffic). Once at Tietê, there are two companies to São Carlos: Empresa Piracicabana (https://www.piracicabana.com.br) or Cometa (http://www.viacaocometa.com.br). There are many buses per day, the price is around R$ 105 and it takes about 3h30min.
Option 2: Take a bus Lirabus (https://www.lirabus.com.br) from GRU to Campinas Bus Station ("Rodoviária de Campinas" in Portuguese). You can buy the ticket in the Lirabus booth at Terminal 2. At Campinas Bus Station take a bus to São Carlos with either Empresa Piracicabana or Cometa (see links above). This option might be faster if you get a good combination of buses - however, if you don't, it might take much longer since there are less buses to São Carlos from Campinas than from Terminal Tietê.
Take a bus Lirabus (https://www.lirabus.com.br) from Viracopos to Campinas Bus Station. From Campinas Bus Station take a bus to São Carlos with either Empresa Piracicabana or Cometa (see links above).