How does Brazil's voting system work?

Brazil's incumbent left-wing president Luiz Inácio Lula da Silva has defeated his right-wing rival Flávio Bolsonaro, overturning a defeat earlier in the electoral process. How did this happen? In Brazil, the president is elected by a simple majority, so in the first round of votes a candidate needs to win more than 50% of the valid vote. But if this doesn't happen, then the top two face each other in what is called a runoff. On 4 October, Bolsonaro won the first round of Brazil's presidential el