summarize how a case is usually heard and decided when it reaches the supreme court
The Supreme Court decides to hear a case based on at least four of the nine Justices of the Supreme Court agreeing to grant the Petition for Certiorari. If four Justices agree to grant the petition, the Supreme Court will consider the case.
The Supreme Court will hear a case if 4 of the 9 justices votes on hearing it. At this point the Supreme Court will look at the case and get ready for the court session on it.