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The House of Representatives elects the President, and the Senate elects the Vice President.
The electoral college
The electoral college that elects the president also elects the vice president. In the event that a new vice president is appointed because of a vacancy, both houses of Congress have to confirm the president's appointee.
The Vice President would then be elected by the Senate.
The legislative branch elects the president
The Conscience.
The electoral college
Electoral College (yes I know its same answer as "who elects president?" but it WAS a different question)
The Congress would decide who the Vice-president would be.
In this case, the US Senate elects the vice-president.
The Vice President takes over.
The registered voters in all the states and DC elect the president and vice-president albeit in an indirect way.