Final answer:
After the Supreme Court agrees to hear a case, both parties submit briefs, followed potentially by amicus curiae briefs. Oral arguments are then conducted, justices deliberate in private, and a majority opinion is eventually delivered, with any dissenting justices having the opportunity to write dissenting opinions.
Step-by-step explanation:
When a case is prepared for oral arguments in court, several steps occur. After a writ of certiorari has been granted, indicating the Supreme Court's agreement to hear the case, the involved parties—petitioners and respondents—submit briefs, outlining their legal arguments. This is followed by potential submissions of amicus curiae briefs by non-parties who hold a significant interest in the case's outcome. Oral arguments are then heard from October through April, scheduled in two-week sessions, where the justices ask questions and engage with the attorneys. Once arguments conclude, justices deliberate in private conferences, take preliminary votes, and discuss opinions on the cases.