"A game that can keep you young and vibrant and all steamed up is a precious thing"
-W.W. "Pudge" Heffelfinger, Yale lineman, (and first ever pro player)
American Football, in all its forms, has been the most popular sport in America for over one hundred years. While professional baseball captured the collective American heart for much of the twentieth century, football at the high school, college, and eventually the professional level ultimately dominated American sports. Friday night high school games remain huge events in many American towns, as they have been for a century; college games were drawing crowds of 100,000 before Babe Ruth took his first professional swing of a bat, and the NFL remains the most followed league in the nation.
The reasons are obvious. It is a grand game and at its best has a sense of drama and theater that no other sport on earth can match.
That said, the drama of football is much more fun if you know what's going on. I have found that most folks who don't know the game are utterly baffled about what they're watching. "Why does one team have the ball and then, seemingly randomly, the other team has the ball?"; "Why do they throw the ball sometimes but not all the time?"
So what follows is an extremely basic (and probably overly dry) explanation of how American football works for those who've never played but might like to.
"Football is a game designed to keep coal miners off the street"
-Jimmy Breslin, Columnist
The American version of football has been played in some form or another for a very long time, perhaps for hundreds of years. Like soccer and rugby and baseball it was first officially organized in the nineteenth century. In its present form American football is essentially based on the English game of rugby.
The main distinguishing features of American football that differentiate it from rugby are the ability to physically block opponents, and the forward pass, both of which are illegal in rugby. The game is also distinctive for it's use of measuring yards on the field to determine when a team must relinquish the ball to its opponent.
Since the game was inherited from the old British universities, it was logical that is was first adapted by similar schools here in the States, specifically Harvard, Yale, Pennsylvania, Princeton, Tufts. However the game soon spread to schools outside the North-East and became as important to the culture of middle class, working class and rural people as it had been to the University set.

19th Century Footballers
Indeed, as other schools, particularly those in the Mid-West became better at the game and the competition more important to alumni, schools like Harvard and Princeton and Yale began secretly paying professional players, the first ever professionals. Even so, by the turn of the century the grip on the game by the "Ivy League" (or "IV", for "four": Harvard, Yale, Princeton and Pennsylvania) was slipping.
The first organized professional football leagues developed in Pennsylvania in coal and steel regions where folks related to the gritty, relentless play on the field.
Gritty indeed! The game was a giant sprawling mess with few rules. At one point Teddy Roosevelt, the President of the nation, actually demanded that the rules be changed to prevent deaths and maimings on the field.
Many of the features of the modern game, such as the forward pass, and yardage markers, came from that decree.
In American football the team with the ball -- the offense -- is given four plays to advance the ball a minimum of ten yards. If the offense cannot advance the ball at least ten yards in four attempts, the other team gets the ball.
In football each attempt is called a "Down" (as most plays result in the ball carrier being "downed" or tackled). So, "first down" is the first attempt; "2nd Down" is the second attempt, etc. All teams will try to advance the ball as far down the field as they can -- they're definately not limited to ten yards on any given play -- but they must move the ball at least ten yards in four Downs or they relinquish the ball to the other team.

This ball-carrier is about to be "downed"
If a team advances the ball ten yards or more, they're given another four attempts in which to go another ten or more yards. For football teams the ultimate goal is to score points, but the main focus along the way is mostly getting first downs. Indeed, while all American sports are obsessed about statistics, American football teams are rated mostly on the amount of yardage gained, or (in the case of defenses), the amount of yardage not given up.
American football is played on a grid. It is all about territory. This seems to be the hardest part of the game for most folks to grasp.

It's important to understand that even if a team moves the ball forty yards in one single play, and they're awarded a new first down, they still have to move the ball ten yards more (within another four plays) or give the ball back to the other team.

So, while a defense can intercept a pass, or recover a fumbled ball, the normal way in American football that defenses stop offenses is by preventing new first downs. If the defense can do that their team gets the ball back.
One hundred yards is a long way to go. A typical offensive series (or "drive") may be successful in moving the ball some of that distance but most times it's eventually stopped.
"When the field gets muddy in baseball, they stop the game. When the field gets muddy in football, the players roll in it like boar hogs"
-Ira Berkow, sportswriter
If a team is successful in moving the ball all the way down the field and they move the ball past the end of the field, into the "end zone", (the goal area), they score a touchdown, which is worth 6 points. A touchdown can be scored either by having a ball-carrier run into the end zone, or, by having a player catch a pass while in the end zone.
Once a touchdown has been scored the team that scores is allowed a Try (often called an "extra point conversion"). A try is usually a kicking play from 2 yards from the goal line. If the ball is kicked through the goal posts it's worth 1 point. However a team can instead attempt a 2-point Try if they want. Instead of kicking the ball through the goalposts from the two-yard line, the scoring team has to successfully move the ball past the goal line (as if it were another touchdown), this kind of Try is worth 2 points.
(Note: in the OFL teams are automatically given the 1 point try, without having to actually kick. Therefore touchdowns are worth 7 points. They can decline the automatic 1 point try and attempt a 2 point try instead. However if they fail this 2 point attempt they are not awarded the 1 point they would've had otherwise and they end up with 6 points instead of 7.)
At any time the offense may decide to kick a Field Goal. A Field Goal is when the ball is kicked off the ground by either a dropkick (where the kicker bounces the ball off the ground and then kicks it), or held by another player, and goes through the goalposts. A field goal is worth 3 points.
(Note: in the OFL the goal posts consist of two players pretending to be goal posts.)
Since a field goal is worth 3 points, (half of a touchdown) and no Try is allowed after a field goal, teams usually attempt to kick field goals only when they reckon they can't score any other way, or perhaps at the very end of game when they trail by 3 points or less and are too far away to reasonably attempt a touchdown. Most field goals are thus attempted on Fourth Down.

A field goal attempt
The only other way of scoring points in American football besides a touchdown, a try, or a field goal is called a safety and is worth two points. A safety occurs when the ball carrier is tackled in his/her own end zone, or the team with the ball purposely or accidentally drops, throws or kicks the ball and it bounces out-of-bounds from inside their own end zone. When this happens the team on defense is awarded 2 points AND gets possession of the ball. While it was originally thought of as a tactical option for the offense, it is fairly rare these days.
"When in doubt, punt."
-Knute Rockne, famous football coach and player
A punt is a kick which, unlike a field goal, does not touch the ground before it's kicked, and cannot score any points. It's a strategic tool meant to force the other team back deep into their own territory.
The punter catches the snap, then drops the ball and kicks it while it's still in the air. In American football once the punt goes over the line of scrimmage it has officially changed possession. A punt cannot be recovered by the kicking team (unless it accidentally bounces off a player of the receiving team first.)

About to punt.
Punting is an important strategic play used when the team with the ball is in a bad field position and is willing to sacrifice possession of the ball for better field position. You see this in rugby and in soccer as well. In soccer a fullback will sometimes clear the ball by kicking it as far as possible into the other team's territory as possible. Same basic concept with American football. If the team with the ball decides that they have too far to go to realistically advance the ball the needed yardage for a new first down, they will punt the ball away. Heck, if you're going to give the ball back to the other team anyway, you might as well have them start as far back as possible.
Punting is almost always done on fourth down, although a surprise punt on third down can be effective. Either way, a good punt can radically change a game.
For the other team (receiving the punt,) a punt is similar to a kickoff -- they goal is to catch the ball and try to run it back as far as they can before being downed.
"Baseball is easy to fathom, not like football, which people explain to me at great length and I understand for one brief moment before it all falls apart in my brain and looks like an ominous calculus problem."
-Eve Babitz, writer
Fair enough.. I'll try to be simple.
In football, the team with the ball will try to score and the other team (without the ball) tries to stop them.
Each team is allowed a series of plays on offense. That may seem sort of obvious but this concept of a series of offensive tries (as in baseball "innings") is a key distinction between the American game and rugby or soccer, or basketball, or hockey, all of which are free-flowing. In those games, teams exchange possession of the ball, back and forth, without any specific structure. Both baseball and American football, however, have rules about when teams are on offense and when they are on defense.
If the team on offense is stopped before they score, the ball is handed over to the other team and other team, now "on offense", tries to score. There are rules that determine when one team must relinquish the ball.
(In most organized football there are entirely different squads of specialist players who play only on the offense or only on the defense. This wasn't always the case but it was found to be more exciting for spectators to have specialists as opposed to have players play on both offense and defense. In the OFL, players play both offense and defense)
Where play starts on the field: Wherever the runner (who caught the ball during the kickoff) was tackled, now becomes the spot where regular play begins. The two teams will face each other at that spot across an imaginary line called the "Line of Scrimmage". The line runs across the field, from side to side like the yard markers drawn on the field. Players cannot cross this line until the ball is put back into play. They line up facing each other like soldiers on an old battlefield.
The play begins: The ball is put into play when one player on the offensive team flips the ball from the ground to another player (usually a player called the "Quarterback"). This toss of the ball (basically a backwards pass) starts the action up again. It's called a "snap" or a "hike". The moment the ball leaves the ground, the action starts again.
The play itself: Once the ball has been "snapped" and the action resumes, players are no longer restricted to one side of the "Line of Scrimmage". Players can go anywhere on the field. The offense will try to move the ball down the field in the direction of their opponents' goal area (the "end zone"), the defense tries to stop them. The Quarterback who has received the snap can either run with the ball can hand the ball to a teammate, or can throw the ball forward to a teammate. If he/she does throw a pass, and it is caught, the play keeps going until the player with the ball is tackled (or tagged) or goes out-of-bounds. Once that happens, all play stops. A new "Line of Scrimage" is created, exactly where the ball-carrier was tackled. The teams line up across from each other from this new Line of Scrimmage again and wait for the ball to be put back into play again with a new "snap".
The Quarterback can throw the ball forward as far as he/she wants but must do so from behind that invisible Line of Scrimmage. If a player with the ball runs past that Line of Scrimmage and then throws the ball forward it is a penalty. However, a backwards pass is legal from anywhere on the field at any time. Once the ball is in play, players could toss backwards passes to each other all the way down the field.
If a forward pass misses the receiver and hits the ground instead or flies out-of-bounds, the play is whistled dead. If a backwards pass misses the receiver and hits the ground, it is still in play, and, like rugby, every one just keeps playing, madly diving for the ball, which often bounces oddly.
Note: A pass from the Quarterback can be caught by players from either team. It is a "live ball" and available to anyone. If a pass by the Quarterback is caught by the opposing team it is an "interception", and can run back the other way for a score for the defense. The same thing happens if an offensive player either drops the ball while running (a "fumble"), or if a backwards pass is misplayed and hits the ground, or if the ball is physically pulled out of the arms of the ball-carrier by a player on the other team. If a ball is "fumbled", it is considered a loose ball and the other team may recover the football. This is one way the defensive team can gain possession of the ball. Defenses try very hard to intercept the quarterback's passes and also to knock the ball out of the other team's hands, causing a fumble.
The more common way of getting the ball back, however, is explained below in the "Downs" section.
The Play Ends: Play is stopped when the runner/pass receiver either has been tackled or runs out-of-bounds; or when a forward pass from the Quarterback hits the ground or flies out-of-bounds. (A pass which is not caught is called an "incomplete" pass.) At that point the ball is considered "dead" and the play is over. The teams line up again at the spot where the runner/receiver was last tackled/tagged. The next play begins when the ball is again "snapped".
"You've heard about the Rubber Band Defense that bends but never breaks? Ours doesn't break either, but it streches 101 yards."
-Don Smith, New York Giants publicist, 1971
An American football field is rectangular -- 100 yards long and approximately 50 yards wide. The field is marked by lines running across it like marks on a ruler. These lines are called "yard lines" and, indeed, are used to mark the field in yardage. The midfield "yard line" is the 50-yard line, as, sure enough, there are 50 yards in each direction to the ends of the field. There are two 40-yard lines; two 30 yard lines, etc.

(The field)
Beyond both ends of the field, are the goal areas, called "end zones". These are ten yards deep.
The point of the game is to advance the ball into this "end zone", thus scoring points, as many times as possible, and then to prevent the other team from doing the same.
Additionally there are goal posts at the back of both end zones and points can also be scored by kicking the ball through these goal posts.
(Note: There are several variations in field dimensions, most notably in the Canadian version of the game, which is longer and wider than the American field. In the OFL the field is seventy-five yards long and usually forty yards wide, and with ten yard end zones. The field is not actually marked.)
"Lord, don't ever phone me the day after a game. I'll either be still getting drunk or lookin' for bail. When you're on a suicide team like I am, you don't wait till next week to start living."
-Mike Battle, New York Jets kick returner
To start a football game, or to restart the game after either team has scored, there is a kickoff. The teams face each other from their respective sides of the field and one team kicks the ball to the other. The other team catches the ball and tries to run up the field as far as they can. The kicking team tries to stop the runner by knocking him to the ground. The "receiving" team tries to protect the runner with the ball by blocking or pushing the other team's players out of his/her way. Once the runner is tackled to the ground, or runs out-of-bounds, regular play begins.
Because both teams send eleven players running with all their might at each other, kickoffs can often be very intense.
(Note: in the OFL there is no tackling. The runner is stopped ("downed") when the opposing team touches him/her with two hands. This is called "tagging" the runner.)