Downs: The most basic rule in football is the Down. Each team, when they are on the Offense (see below) has the task of moving the football ten yards in four plays. If the team does not get ten yards in THREE plays, they usually have to kick the ball away to the other team, and then they are back on the defense. This may sound easy to move a ball a measly ten yards, but with every player on the Defense trying to stop the runners and receivers, it can be a real challenge! Getting a First Down is one of the main goals for a team's Offense, because they get four more tries at moving the football, and do not have to kick it away.
Offense: The Offensive side of a football team is comprised of many key players, trying to move the football down the field to score. The key positions to look at on this aspect of the team are the Quarterback, the Running Back, the Wide Receivers, and the Offensive Linemen. The Quarterback is the one in the middle, behind the Offensive Linemen, and he is responsible for orchestrating most of the plays when the offense is on the field. He takes the snap (the ball) from the Center Lineman, and he has the choices of giving it to a Running Back, throwing it to a Wide Receiver, or carrying it himself. There are of course hundreds of variations on this action, but the main idea is for the Linemen to block the Defense from getting to the Quarterback, so that he can complete the play and get a First Down.
Defense: The Defense of a football team is comprised of a Defensive Line and a few men called Safeties. The Linemen are the big guys trying to get to the quarterback, and the Safeties are the fast men on the outside trying to stop the Wide Receivers from catching the ball. It is the job of the Defense to stop the Offense from moving the ball ten yards in four plays to get a First Down. If they succeed, the Offense has to kick the ball back to their team. The Defense is also trying to get the ball! If they succeed in catching a ball or forcing the Offense to drop the ball and then pick it up, it is called a Turnover, and the team's Offense comes back out to try for more points.
Special Teams: Any member of the football team can be on the Special Teams Unit. Special teams come out onto the field for certain plays during the game. The key players to look for are the Kicker, the Punter and the Kick Returner. When there is a Kickoff, Field Goal attempt, a Punt (kicking the ball away on fourth down) or a return of a Punt or Kickoff, the Special teams will come on to perform these specific tasks. Special teams are very important a football game's outcome. Many times the three points earned off a Field Goal (see scoring) will determine the winner of the game, and starting field position for the Offense is key.
Scoring: There are only ways to score points in a football game, but it can seem a bit complicated if you aren't familiar with the game. A Touchdown is the ultimate goal of the football team when trying to score because it earns six points and gives the team an opportunity to score either one or two MORE points on the next play, called the Extra Point Attempt. In most situations a team will kick the ball through the goal post on this play and earn one extra point, for a total of seven points. If they decide to go for TWO points, the ball is snapped from the two-yard line, and the offense and the quarterback must get the ball into the end zone just as they did for the touchdown. A Field Goal scores three points and is performed by the Kicker on the team (see Special Teams). He has to kick the ball from a spot on the field through the goal posts. The only other scoring in football is called a Safety, which is worth two points, but it is an uncommon score. Two points are awarded to a team if their Defense manages to down the football in the opposing team's end zone.
Penalties: There are many different types of penalties in football, and they are called by the Referees, (the guys in the stripes monitoring the game!). If a penalty occurs, the Referee will throw a yellow flag onto the field, stopping the game play and the time clock. Penalties vary from 5 to 15 yards, depending on the severity of the foul. Sometimes the team that is penalized also loses one of their precious Downs, which can also force them to kick the ball away. The most common penalties are False Starts (5 yards, repeat the Down), Offensive Holding (10 yards, repeat the down), Defensive Interference (15 yards, and the ball is placed where the foul happened). All penalties are announced by the referee during a game, so if you are confused, just listen to the announcement.
In conclusion, I hope that I have helped explain some of football's basic rules and procedures. Watching a game is really the best way to learn the intricacies of the game, but now that you have some basic understanding, I hope that you learn to love the game as much as I do!