BRASÍLIA—Now that the Olympics are winding down, Brazil’s attention returns to its long-running political drama as the country’s Senate starts the final phase of suspended President Dilma Rousseff’s impeachment trial—a proceeding widely expected to permanently remove her from power.

During the trial, set to begin on Thursday, Ms. Rousseff will face charges that she illegally masked the country’s growing budget deficit through accounting tricks. She has denied the charges and said the accounting was lawful. A conviction by...