When a team has possession of the football, it can score points in several ways. Touchdowns, extra points, two-point conversions, field goals, and safeties all can increase a team's score.
Touchdowns
A touchdown is worth six points — the ultimate goal. A team scores a touchdown when an offensive player carrying the ball, or a defensive player who has obtained the ball from the other team after recovering a fumble or intercepting a pass, advances from anywhere on the field and breaks the plane of his opponents' goal line with the ball. The ball just has to cross the line.
A team is also awarded a touchdown when any player who's inbounds catches or recovers a loose ball behind his opponents' goal line. This sort of touchdown can occur on a kickoff, a punt, or a fumble.
Extra points and two-point conversions
A try for an extra point is attempted during the scrimmage down that's awarded after a touchdown. The extra point is successful when the kicker kicks the ball between the uprights of the goalpost and above the crossbar, provided that the ball was snapped 2 yards away from the opponents' goal line (or 3 yards away in high school or college). Teams should almost always make their extra point attempts — especially above the high school level — because the kick is a fairly easy one.
When a team is feeling particularly confident — or desperate — it might instead attempt a two-point conversion after scoring a touchdown. The offense gets the ball on the 2-yard line (the 3-yard line in high school and college) and must advance the ball across the goal line as if scoring a touchdown.
Field goals
A field goal, often the consolation prize for an offense that stalls within its opponent's 30-yard line, is worth three points. A team scores a field goal when a kicker boots the ball entirely through the uprights of the goalpost without touching either the ground or any of his teammates.
Safeties
A safety is worth two points. The important factor in a safety is impetus, which is the action of an offensive player that gives the ball momentum. A safety is awarded to the defending team if it sends the ball into its opponent's end zone and the ball becomes dead without changing possession. This occurs when a quarterback, running back, or receiver is tackled with the ball in his own end zone or goes out of bounds behind the goal line. A safety also is awarded when the offensive team commits a penalty that would otherwise require it to have the ball marked in its own end zone.
A safety is also awarded when a blocked punt goes out of the kicking team's end zone. And if the punt receiver muffs the ball and then, when trying to retrieve the ball, forces or illegally kicks it into the end zone (creating new impetus) and it goes out of the end zone, the defensive team is given a safety. If a muffed ball is kicked or forced into the end zone and then recovered there by a member of the receiving team, the defensive team is awarded a safety.