Appointing a new judge to the supreme court. how are the legislative and executive branch involved in the process?

In appointing a new justice to the Supreme Court ...

The Executive Branch of government is involved by nominating the candidate for the role of Supreme Court Justice.The Legislative Branch of government is involved by confirming (or denying) the appointment of the candidate nominated by the President.

The way that Supreme Court justices are put into office is stated in Article II, Section 2 of the Constitution:

He [the President] shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law.

Of the revolutions of 1848.