The house of representatives
To nominate candidates.
The President, the Vice President, and members of Congress.
The President has to nominate someone to be Vice President, but that said person can only be Vice President with the majority vote of both Houses of Congress
They nominate before every election, which is every four years.
The new president will nominate someone for vice-president and if Congress approves, the nominee will be the new vice-president.
he would nominate somebody and then get that decsion approved by the house of representatives and the senate
After John Kennedy's assasination, the 25th Amendment was enacted stating tha the President would nominate a replacement which would have to be approved by a majority vote of the House of Representatives and Senate. Previously, the position was left unfilled.
Biden would then nominate someone to be vice-president and if he is confirmed by both houses of Congress he would be the vice-president.
if the president dies the vice takes over
The President will nominate a new Vice President, who must be confirmed by both houses of the Congress in accordance with the 25th Amendment. (see related link)
Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress.
The president nominates supreme court justices. (also "technically" the president selects the vice president "after" he is elected, so the president "sort-of" nominates the vice president too.) . Hope that helps.