In the ordinary case, the people vote on election day and, often, before election day, either by mail or through “early voting” that happens before November 3. But November 3 is the cut-off: it’s the last day to vote, and, when the polls close in a state, the results may start to be released.
Each state has a procedure of regulating and policing the count. (You can see a table listing those procedures here.) After the count is completed, the winner is certified and the electors associated with the winning candidates are appointed to vote in the electoral college. In all but two states (Maine and Nebraska), the winner of the vote in a state gets all of the electoral votes from that state. In Maine and Nebraska, the winner of each Congressional district gets one elector, and the statewide winner gets two.