The curl is another way to strike the soccer ball. Instead of getting the ball straight to the target, you kind of want to curve the ball or bend the ball around an obstacle, usually the wall when you have a free kick, or around the opposition's player during a corner kick, or even when you run after dribbling and want to get it around the goalkeeper from a different angle.
So to curve the soccer ball, instead of hitting the ball in the center on, you kind of want to get some spin on the ball by hitting the ball slightly on the side.
It can be with the shoe laces, it can be with the inside of the foot, it doesn't matter. But it has to be off-center so that you get some spin on the ball.
For example, if you get it on the outside, the ball's going to curve away from, could curve away from the goalkeeper into the far angle of the goal instead of going straight at him.
To curve the ball more successfully you want to make sure that after you hit the ball you follow-through, and the follow-through crosses the opposite leg.
So instead of following-through straight with the ball, you follow through and give the ball the right motion, the right movement, by crossing over to the opposite leg after you follow-through with the shot.
And these are some of the basics of how to execute the curl.