Clause one is a "vesting clause," similar to other clauses in Articles One and Three, but it vests the power to execute the instructions of Congress, which has the exclusive power to make laws; "To make all laws which shall be necessary and proper for carrying into execution the foregoing powers, and all other powers vested by this Constitution in the government of the United States, or in any department or officer thereof."
The head of the Executive Branch is the President of the United States. The President and the Vice President are elected every four years.
Clause 2: Method of choosing electors
Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.
Under the U.S. Constitution the President and Vice President are chosen by Electors, under a constitutional grant of authority delegated to the legislatures of the several states and the District of Columbia (see Bush v. Gore). The constitution reserves the choice of the precise manner for creating Electors to the will of the state legislatures. It does not define or delimit what process a state legislature may use to create its state college of Electors. In practice, the state legislatures have generally chosen to create Electors through an indirect popular vote, since the 1820s.
In an indirect popular vote, it is the names of the electors who are on the ballot to be elected. Typically, their names are aligned under the name of the candidate for President and Vice President, that they, the Elector, have pledged they will support. It is fully understood by the voters and the Electors themselves that they are the representative "stand-ins" for the individuals to whom they have pledged to cast their electoral college ballots to be President and Vice President. In some states, in past years, this pledge was informal, and Electors could still legally cast their electoral ballot for whomever they chose. More recently, state legislatures (exercising their constitutional authority to do so) have mandated in law that Electors shall cast their electoral college ballot for the Presidential Candidate to whom they are pledged. The constitutionality of such mandates is uncertain.
Each state chooses as many Electors as it has Representatives and Senators representing it in Congress. Under the Twenty-third Amendment, the District of Columbia may choose no more electors than the state with the lowest number of electoral votes. No Senators, Representatives or federal officers may become Electors.
Clause 3: Electors
The Electors shall meet in their respective States, and vote by Ballot for two Persons, of whom one at least shall not be an Inhabitant of the same State with themselves. And they shall make a List of all the Persons voted for, and of the Number of Votes for each; which List they shall sign and certify, and transmit sealed to the Seat of the Government of the United States, directed to the President of the Senate. The President of the Senate shall, in the Presence of the Senate and House of Representatives, open all the Certificates, and the Votes shall then be counted. The Person having the greatest Number of Votes shall be the President, if such Number be a Majority of the whole Number of Electors appointed; and if there be more than one who have such Majority, and have an equal Number of Votes, then the House of Representatives shall immediately chuse [sic] by Ballot one of them for President; and if no Person have a Majority, then from the five…