American football is believed to be derived from the highly popular, similar game of rugby. It wasn't until Walter Camp that the rules changed to a more recognizable format. Camp is deemed un-officially, the father of football. The most important of the changes that he introduced were the line at which the players started (line of scrimmage) and the 1st down distance.
A man nick named Pudge was the first man to actually e paid to play the game, during a match between Allegheny and Pittsburg in which the sum was 500 dollars. The exchange of money could be charted as the first "pro football contract".
1932 was the first NFL playoff game. It was at this time that yard lines were introduced as well as the repositioning of the goal post.
Even before rugby, there was a similar game in Rome in which the 2 were believed to stem from. The game was called "Harpastum". The game was played with a hard, softball sized ball and was deemed to be very aggressive.