People who are newcomers to this country, or who are interested in the NFL's proposed European expansion to London, England might want to brush up on the nuances of how to follow a game.
There's usually a certain amount of looking down one's nose at the other branch of "football" - Europeans and others refer to it dismissively as "handegg", and wonder what the big deal is about. For people used to a sport being dynamic and going back and forth, the start/stop nature of American football can be maddening. But here's how someone not new to the game can understand why its fans are so passionate, instead of seeing it as a random collection of out of shape men crashing into each other.
First, a very, very brief rundown of enough of the game's rules/ideas to give some context. There will be some shorthanding and some oversimplifications, but it's necessary to not overcomplicate the matter and to make this self-contained and an overall beginner's guide.
There are two teams playing, one playing "offense" and the other playing "defense". The goal of the "offense" is to move the ball over the goal line at the opposite end of a hundred yard field. The goal of the "defense" is to stop them. That being said, the "offense" can score in one of two ways: either to kick the ball between the uprights of a goal in the middle of the "end zone" (beyond the goal line but in the field of play) referred to as a field goal and worth three points, or by carrying or catching the ball beyond the goal line but still within the field of play. This is referred to as a "touchdown" and is worth six points. After a touchdown, the team can elect to kick a field goal for a further point, or attempt another touchdown for two points. The former is pretty much automatic, the latter is a bit riskier but comes into play if the team is behind.
The offense has four "attempts", or "downs", to move the ball ten yards. When the announcer says "first and ten" he's referring to the number of the down, followed by how many yards the team must move the ball downfield to get another "first down". They can do this either with a passing play, in which the quarterback throws the ball to a receiver who then runs as far as he can (or simply fair catches as he's tackled), or with a running play, in which the offensive line attempts to physically displace players in the way, with one member of the team trying to run the ball forward. The goal of the defense is to contain the forward movement of the ball. If the offensive line has not moved the ball forward by ten yards at the end of four downs the defensive team becomes the offensive team and gains possession then and there. If an offensive line does not think it can achieve this, on the fourth down it will kick the ball downfield (punting) in order to try and restart the game as far away from their own goal line as possible. Sometimes a team will risk a fourth and one to try and move that final yard and beyond, and fail - and turn the ball over on downs to the other side, sometimes in a very bad field position for that team (when desperate).
The defensive line can also catch the ball intended for a receiver (an interception), which gives them IMMEDIATE control of the ball as the offensive line (in fact, the receiver can and sometimes does run the length of the field for a touchdown) or if the ball is dropped by a player (known as a fumble), they can grab/recover it if it is still moving and depending on whether the player is standing or prone when this happens, run the ball for a touchdown or simply stay put, giving the defensive line possession. This kind of changeover is called a turnover. This is especially disastrous when it happens close to the offensive line's goal line because it puts the team, now in defensive mode, within only a few yards of a touchdown, and certainly within field goal range.
Here are some points which make the game far more interesting.
Players don't really have set positions on the field*. They basically exist as chess pieces: the receivers are nimble and able to run and catch a ball, the linemen are large slabs of human meat designed to either be an unmoving object or an unstoppable force, and the quarterback exists to either run, hand off, or throw the ball, as well as co-ordinate the play. There is no set way to set up players on that field - unlike hockey, where there's three guys up front, two behind, and a goaltender, so long as all players are behind the line of scrimmage, they can stand where they want. Therefore coaches design formations in advance and ways that they'll move, both offensively and defensively, called "plays". The offense selects a play, the defense reacts to it by forming a counter-formation trying to guess intent. The quarterback can either run the called play or announce real-time adjustments in his instructions to teammates, shouted in a code. You generally have a rough idea of what they'll try and do by the formation - spread out men means an attempt to throw, compact phalanx means a running play. Sometimes the formation is deceptive, and what looks like a passing play is a fake for a run, or the blocking starts in earnest in time for the quarterback to quickly throw to a player who breaks away without warning.
This can also be moderated by other constraints. If a player that is key to certain types of play is injured or unavailable, then adjustments have to be made. Typically a team at 3 and 17 will try to throw the ball to get the most possible yardage to get the first down, and a team at 3 and 1 will simply try and conservatively run the last yard. But given that the United States has regions whose climates vary considerably, sometimes a team used to playing in Miami (warm, humid) will have difficulty in Minnesota (brutal cold and falling snow), and Green Bay (cold, wind, ice) might find New Orleans a challenge (humid and very hot), a snowfall might make players slip too much to execute a run game or a long pass.
The other factor to consider is time. Given that the ball is in the possession of one team until the ball is turned over, if one team is vastly ahead it can run slow-moving running plays that chew up clock time, making the amount of time left to play just as much an enemy to a team as the opposing side. If a team is quite behind it might have no other option than to opt for riskier plays, longer throws, more aggressive runs - moves that are easier to spot and easier to defend. In some instances, desperate to make up a deficit, a team at four downs and four yards might try an "onside kick" - in which the punt is not kicked far downfield, but barely - to try and give the offensive line a chance to grab the ball before the defense and regain control of the ball for four more downs. This can backfire with disastrous consequences.
So realistically speaking, what you're watching is a game of chess - a game plan, orchestrated in advance by two coaching staffs - selected by the coaches, modified by ambient conditions, tweaked on the fly, and maybe even over-ruled at the last minute by players because of emergent circumstances. It can make for some extremely exciting play.
Of course, there are other considerations as well. Typically before a game people will park a truck with a barbecue or grill in the parking lot and grill or consume food and have a pre-game party, referred to as a "tailgate". Certain teams' fans are known for colorful or odd traditions - Wisconsin is known for cheesemaking, so Green Bay Packers fans often wear foam helmets resembling cheese. (Sometimes their opponents' supporters will wear hats shaped like cheese graters). Seattle Seahawks fans refer to themselves as "the 12th man" and try to cheer their team to success with deafening results. Oakland Raiders fans typically look like something out of a Gwar or Road Warriors video, spikes and shoulder pads, clubs and chains - row after row of heavily painted black and white, the team's colors. New Orleans Saints fans often wear costumes reminiscent of Mardi Gras with brass bands and such. Atlanta Falcons fans have been guilty of leaving games at halftime.
If you're watching at home: bets have been made, beer has been consumed, prayers have already been said at the faith community of choice of the respective fans. Chips and chicken wings are laid out, and the big screen is turned on.
In short it's a colorful riotous display, enormous amounts of noise, and an evolving story that changes with the rise and fall of scores and stats. 11 men line up against 11 men, and bones crunch and bodies slam into each other. It's Sunday, and anything can happen.
To amp up the experience more, try college football.
To really amp up the experience, the Super Bowl is played once a year, in February.
* This is a simplification. There is a rule that there must be at least seven players on the line of scrimmage, and no more than four behind them. The point is, how they're arranged is not mandated.