Which president was the first one elected by the common people?

No US President has ever been publically elected. Presidents are elected by the electoral college, not the public.

The electoral college is made up of special "electors" who are chosen by each state. Every state has a number of electors equal to the number of Representatives and Senators they have in the US Congress- it will always be at least three (every state gets two Senators and at least one Representative). Right now, Vermont has the least with three, but California has the most with a whopping 55, while Texas has 38.

On election day, the public doesn't vote directly for the president (even though when you vote, it seems like you are); they are actually voting for which candidate they want their state's electors to vote for. 48 of the 50 states give all of their electoral votes to the candidate who wins the most votes in their state (Maine and Nebraska allow the electors to be split up). Then all of the electoral votes are added up; whichever candidate wins the most electoral votes is the new president-elect.

This is why states like Florida, Pennsylvania and Ohio tend to be very important during Presidential elections. Most states tend to vote for one party or the other- for example, most of the South tends to vote for Republicans; California, New York and New England usually vote for Democrats. Florida, Pennsylvania and Ohio don't always vote for the same party- for this reason, they are nicknamed "swing states" (because they can "swing" either way). These swing states tend to get bombarded with political ads, speeches and rallies, as candidates seek to win their valuable electors.