First, I recommend reading the United States Constitution.
These people are called the Electoral College, and the electors are determined by each state's Secretary of State, who has a slate of electors for each political party.
Depending on who wins, and whether or not the state is a winner-take-all state or proportional state, the Secretary of State from that state certifies whichever slate gets the votes.
If you want to be an elector, become a player in whatever political party you want. Typically electors are Members of Congress, and other high-ranking State Assemblymen/Assemblywomen and State Senators.
Edit: The reason no "average" person can be an elector is because if you read The Federalist Papers, the whole reason for having The Electoral College was to prevent the common people from electing a tyrannical idiot to the Presidency.