The people do not elect the president, that is what all the brouhaha around the Electoral College is about. By convention, each state has agreed that the people vote for who their state is going to vote for - but that is not constitutionally required.

This turns out to be really helpful when someone starts claiming something like widespread voter fraud for instance, because there is no one institution to attack, or even identical set of rules that can be exploited. Each state runs it's elections as it sees fit, and then votes the way it deems necessary - and is strongly interested in making sure it's voice is heard.