Each lawyer writes and submits a brief (a written argument) before the actual court date. The Justices read and consider each brief before the case is heard in Court. This allows each Justice to have prepared questions to ask the lawyers when they appear.
When the day of the hearing arrives, each side is given time, usually slightly less than an hour, to present its case.
When the oral arguments have ended, the Justices meet to render a decision. The Justices then present their individual decisions and offer the majority decision of the Court. Each Justice writes a concurring or dissenting opinion of the Court.