Supreme Court Appointment Process: President's Selection of a Nominee [Updated September 28, 2020] [open pdf - 1MB]
From the Summary: "The appointment of a Supreme Court Justice is an event of major significance in American politics. Each appointment is of consequence because of the enormous judicial power the Supreme Court exercises as the highest appellate court in the federal judiciary. Appointments are usually infrequent, as a vacancy on the nine-member Court may occur only once or twice, or never at all, during a particular President's years in office. Under the Constitution, Justices on the Supreme Court receive what can amount to lifetime appointments which, by constitutional design, helps ensure the Court's independence from the President and Congress."
CRS Report for Congress, R44235
Congressional Research Service: https://crsreports.congress.gov/