Formations (The way players line up before the snap)
Offensive formations The offense tends to line up more blockers in very short or very long yardage situations. In short yardage situations, the defense will be expecting a run and will rush the line of scrimmage with as many players as they can spare. In long yardage situations, offenses will most likely attempt deep pass plays and will want to ensure the receivers have ample time to get downfield and that the quarterback has time to make an accurate throw.
The fewer linemen an offense has, the more wide receivers or backs it can have. This gives the quarterback more targets or the rusher more blockers. The offense is constantly trying to sub players from the bench in between plays to ensure that the optimal players for each situation.
Generally speaking, the more receivers are out on the field before the snap, the more likely it’s going to be a pass play.
Defensive formations In it's crudest terms, defenses can be categorized into two groups. Run defense or pass defense. In run defense, the defense tries to crowd the line of scrimmage to eliminate gaps for runners to move up the field through. Pass defenses are broken down into zone or man to man. In zone coverage, each player is responsible for covering a small area of the field. Man to man, as the name implies, is one to one coverage.
The defense is constantly trying to guess what type of play the offense will run. There is also the option to blitz. In a blitz play, the defense sends players at the opposing team's quarterback in an effort to break his concentration or bring him down behind the line of scrimmage. The risk is that there are less players downfield in the event of a completed pass, meaning a completed pass could give up more yards.