When oral arguments are concluded, the Justices have to decide the case. They do so at what is known as the Justices' Conference. Two Conferences are held per week when Court is in session, on Wednesday and Friday afternoons. The Justices vote on cases heard on Mondays and Tuesdays of a given week at their Wednesday afternoon Conference. The Justices vote on cases heard on Wednesday at their Friday afternoon Conference. When Court is not in session, usually only a Friday Conference is held.
Before going into the Conference, the Justices frequently discuss the relevant cases with their law clerks, seeking to get different perspectives on the case. At the end of these sessions, sometimes the Justices have a fairly good idea of how they will vote in the case; other times, they are still uncommitted.
According to Supreme Court protocol, only the Justices are allowed in the Conference room at this time—no police, law clerks, secretaries, etc. The Chief Justice calls the session to order and, as a sign of the collegial nature of the institution, all the Justices shake hands. The first order of business, typically, is to discuss the week's petitions for certiorari, i.e., deciding which cases to accept or reject.
After the petitions for certiorari are dealt with, the Justices begin to discuss the cases that were heard since their last Conference. According to Supreme Court protocol, all Justices have an opportunity to state their views on the case and raise any questions or concerns they may have. Each Justice speaks without interruptions from the others. The Chief Justice makes the first statement, then each Justice speaks in descending order of seniority, ending with the most junior justice—the one who has served on the court for the fewest years.
When each Justice is finished speaking, the Chief Justice casts the first vote, and then each Justice in descending order of seniority does likewise until the most junior justice casts the last vote. After the votes have been tallied, the Chief Justice, or the most senior Justice in the majority if the Chief Justice is in the dissent, assigns a Justice in the majority to write the opinion of the Court. The most senior justice in the dissent can assign a dissenting Justice to write the dissenting opinion.
If a Justice agrees with the outcome of the case, but not the majority's rationale for it, that Justice may write a concurring opinion. Any Justice may write a separate dissenting opinion. When there is a tie vote, the decision of the lower Court stands. This can happen if, for some reason, any of the nine Justices is not participating in a case (e.g., a seat is vacant or a Justice has had to recuse).