Question

no gain on fourth down intergers

Answer 1

I THINK it means that the team with the ball gained no yardage on their last chance to move the ball 10 yards and start over again at a first down. Since they failed to gain any yardage or the necessary 10 yards to keep the ball, they now have to turn the ball over to the other team who will start trying to gain 10 yards in the opposite direction. 

I'm not sure how the other team gets the ball, though, as in: Does this team have to kick/throw it to them or do they simply hand the ball over.