Typical game line up: Two teams try to place a ball in some place that the other team is trying to make sure the ball never goes. When the other team gets the ball, the exact same thing happens except flipped around.
(Watch some demo clips on YouTube if you are bad imagining)
So there's offense and defense. Offense has a straight line of people that are trying to break up the defending line of people through coordinated movements so that the ball carrier can run past the line of defense. The defense is trying to break through the offense in a similar coordinated movements so that people standing behind the line of defense (linebackers, easy to remember) can run through the offensive line and deny the ball carrier.
For example, the defensive lines coordinates all of the linemen to split the offensive line down the middle, a linebacker runs through the opened space and knocks the ball carrier (should he still be there) into the next lowest draft pick. Main form of moving your average six foot one, two-hundred fifty pound linemen is to run a similarly sized man into his face and try to overcome him before he overcomes your guy.
Offense is different because they have possession of the ball, lack any linebackers, and can actually throw the ball. Their plan isn't to out-meat the defense, but to distract the defense enough so that the quarterback can pass the ball to some other ball carrier, and the ball carrier can run through an opened spot that the linemen temporarily opened up. The second the ball touches the ground, that play is finished, the next play starts at the closest yard to where the ball initially dropped.
Offense has four 'plays' (called downs) to move the ball forward a total of ten yards, or ten meters. Every ten yards, the down counter is rest back to one, until the possession of the ball is lost, the offense runs out of downs, or if offense scores. Sometimes, if the offense is certain it can't get past that ten yard marker, they will punt the ball, giving possession of the ball back to the defense, but first by kicking the ball as far away from their own endzone as they can.
Scoring is mainly done with touchdowns (six points), running the ball into the endzones (the end of a field) of the opposing side, but can be done in safeties (two points) (a reverse touchdown of forcing a team into their own endzone), field goals (three or one points) (kicking the ball in between the "|_|" shaped poles), and conversions (two points) (exact same thing as a touchdown, but different). After a touchdown, offense lines up again around ten yards from the enemy's endzone and has a chance to make a one-point field goal (easy) or a two-point conversion (significantly harder).