The U.S. Constitution lists no requirements. There are no specific requirements to be appointed as a justice per the Constitution, but most nominees have followed a similar background in the law and the nominee has to be approved the U.S. Senate.
The president nominates justices. Nominees have to be trained in the laws of the United States and nearly all have attended law school. Common professions represented have been members of Congress, governors and members of the president's cabinet of advisers. Presidents are likely to nominate someone with whom they are familiar. Nominations are sent to the Senate Judiciary Committee.
The president's nomination must be confirmed by the Senate, which will vote to determine if the nominee is well-suited to the position of justice on the Supreme Court. The selection must receive a simple majority vote to receive a lifetime appointment as a justice.