Each Team is made up of 3 teams; the offensive, the defensive and the specials.
Offensive Team and Scoring.
The offensive team are on the field when the team have possession of the ball and their main objective is to get the ball down the field to the end zone and score a touchdown in as few 'plays' as possible covering as much yardage as possible in each play. The Quarterback is on the offensive team, his main job is call plays and find openings down field with his team mates to get the ball as far and as safely as possible. Each play has 4 downs. Every time the offensive team successfully completes a play it goes back to 1st down. The current down is displayed with an arrow on screen with a number following it. A 1st down is always "1st&10" this means that they have to gain 10 yards towards the end zone to earn another 1st down. they must successfully make contact (with say a knee) with the ground without dropping the ball, if they drop the ball before they've hit the ground the ball is "live" and the offensive team must pick it up before the defensive team does or it will cause a turnover (turnovers will be explained more under defensive team). If they only gain 5 yards, for example, then it becomes 2nd down and as they still have 5 yards to gain before a 1st down then it becomes "2nd&5". If they don't manage all 5 yards then it becomes 3rd down and so on. On 4th down they can either continue and try and get a 1st down, attempt a field goal (which brings on the specials team) or make a punt and kick the ball up field towards the end zone they are scoring in in an attempt to make the distance the other team has to travel to make a touchdown as long as possible. If the offensive team makes a successful play and the ball is either caught by one of their players in the end zone or one of their plays successfully runs into the end zone then the team scores a touchdown which earns them 6 points.
Once a team has scored a touchdown they have the chance of a conversion that can be played in two ways. They can try for another touchdown which earns the team a two point conversion, meaning their touchdown is now worth 8 points or a kick conversion which earns the team a one point conversion and makes their touchdown worth 7. Unless a team is desperate to increase their lead or feeling particularly confident and comfortable with the lead they already had most will choose to take the kick over the touchdown conversion as it is far easier to score. This ends play and typically means possession goes to the other team.
To score a field goal the kicker must kick the ball from wherever the last play ended through the veritcal bars in the end zone. If this is done without the defensive team blocking the ball then the team scores 3 points. This ends play and typically means possession goes to the other team.
To determine how far up the field the other team will have to travel with the ball to score a touchdown the team who previously have possession will kick the ball down field as far as possible. If the team about to take possession catch the ball within the endzone or the 20 yards before the end zone they can drop a knee to ground meaning the accept to start at the 20 yard point (this is 80 yards from the end zone they score into) or begin running. The team who kicked the ball will then try and stop the catcher as quickly as possible so the offensive team will have to travel as far as possible to score. To start from the distance they make when running they must successfully make contact (with say a knee) with the ground without dropping the ball, like with successfully completing a play and earning a first down. If they catch the ball further up field than the 20 yard line they can either take a knee and say they want to start from there, or again, begin running. If the team that kicked the ball catch it then they have possession and again can begin running back up field to make the distance to the end zone as close as possible. This is normally down by using a short, across field kick rather than a long down field one.
Defensive Team and Turnovers
The main objective of the defensive team is to defend their endzone and prevent the other from scoring. They can do this in several ways:
They can sack the quarterback to the ground preventing him from passing the ball and normally making the next down longer than that one as the quarterback is generally 5 yards behind the point of play.
They can sack the receiver (person who receives the pass from the quarterback) meaning that the point they hit the ground is the new point of play. The sooner they do this the better. If they do it before the yardage that earns a 1st down for the offensive team then they cause a 2nd down (or 3rd or whatever they were up to).
They can stop the catch by hitting the ball and making the play in complete or, if they catch the ball themselves they will start running towards their own scoring end zone as they will have caused a turnover and gained possession.
If the ball is dropped before the receiver has hit the ground the ball is still live and if the defensive team can pick it up and turnover possession. To make this as advantageous as possible they, like with a stealing catch must begin running towards their own scoring end zone. Wherever they drop to the ground is where play for the offensive team begins. If they make it all the way to the end zone, it is a touchdown.
Most common illegal plays/fouls
These are the most likely illegal moves you will see in a game.
Holding - Preventing a player of the opposite team from moving during play by gripping their arms or shirt for prolonged periods of time.
False Start - A player moving before the snap.
Off side - Player in an illegal position during play.
Unnecessary Roughness - A tackle or injury of a player not relevant to the play. E.g. sacking or head butting a player to the ground when neither of you have possession.
And I can't remember the term for this one but it is an illegal move to have your hand in the face guard of another player.
Illegal plays/fouls normally result in creating a first down or shortening yardage if the offending player is on the defensive team or increasing yardage (normally by another 10 yards) if it is a player on the offensive team who committed the foul.
Other things to know
The game is in 4 quarters. Each quarter lasts 15 minutes but the game clock stops whenever the ball isn't in play.
Each team has 3 time outs per half.
Penalties are "flagged" by one of the refereeing team throwing a yellow flag onto the field at roughly the point the penalty happened.
Coaches can query a referee decision by throwing flags (normally in their team colours) onto the field. The referee will then go and watch the instant replay under the hood. He has 1 minute to reach a decision but can stay under longer if he is going to overturn the decision in order to adjust the game clock and work out where this means the ball is in play from when play resumes. The referee is on mic so he will explain his decision when he comes back onto field.
If the referee overturns the decision after a coach asks for review then the team do not lose a time out. If after review the referee sticks to his original decision then the team will lose one.