The President nominates someone for a spot in the Court and must face a series of hearings in which both the nominee and other witnesses make statements and answer questions for the Senate Judiciary, they then vote to send the nomination to the full United States Senate. The Senate votes to pick which person will be in that position, this requires a simple majority. This way, both the Executive and Legislative Branches of the federal government have a voice in the Supreme Court.
The Constitution explicitly assigns the president the power to sign or veto legislation, command the armed forces, ask for the written opinion of their Cabinet, convene or adjourn Congress, grant reprieves and pardons, and receive ambassadors.
