Do the US people directly elect the President?

No, the people of the US do not directly elect the president. There is a group known as the Electoral College which actually elects the President and Vice President, after being selected as proxies in the popular election. It has occurred that Presidents were elected by the electoral college vote who did not receive a majority of the popular vote nationwide.

Each political party in a state chooses a slate of electors. There are as many for a given state as a state has both US senators and US representatives in Congress. In 48 states, all of a state's electoral votes go to the single party that receives the most votes (President and Vice President). In Maine and Nebraska, some may go to the other candidates based on the vote. The electors from across the country meet in December and officially cast their votes for their candidates, and these votes are delivered to Congress to be tallied on the following January 6. If a Presidential candidate receives 270 of the 538 total electoral votes, he is declared elected, along with his Vice President, and sworn into office on January 20. If no candidate has enough votes, the House will elect the President and the Senate will elect the Vice President.