A touchdown is scored when the football crosses the plane of the goal line – the white line separating the end zone from the rest of the field. If the ball – with or without the ball-carrier – crosses that line while an offensive ball-carrier is in possession of it, it’s a touchdown. If the ball is being thrown into the end zone and is caught by a receiver, the receiver needs to have two feet down in bounds and have full control of the ball to be called a touchdown.
Touchdowns are worth 6 points. Teams usually opt to kick the point after (PAT, Point After Touchdown) but can also choose to “go for 2” – get the football into the end zone from the 2-yard line for 2 points.