Try to get to the end zone, if you do you score 6 points. You have 4 attempts to move forward 10 yards, if you don't, the ball goes to the other team. If you have more points, you win.
That's it, that's all you need to know to watch it and enjoy it. Sure, there's more ways of scoring and the details of each position, the routes they are running and play-calling in general is interesting, but it's not needed to just watch the game.