For our lessons we use the Step Method developed by Rob Brunia and Cor Van Wijgerden. All information about this teaching method can be found at www.stappenmethode.nl.
The nice thing about the Step Method is that it is the common thread of chess training. But with taking the lessons and doing the exercises alone, you are not going to make much progress as a chess player. You can only get better by playing real games regularly. This gives you the chance to actually apply what you have learned in the lessons in a game. And this is not easy, because after every move in a game you have to make a new task as it were ... find the strongest move.
You can practice with other kids from the club, but participating in tournaments outside the club is also possible. For example, there are regular tournaments for beginners, the so-called 'debutant tournaments'. In Flanders there are also 11 youth tournaments which are part of a 'criterium'. As a club we participate in most tournaments and transportation is provided.
What is certainly as important as playing games is "analyzing" them. This means going over the moves you played with a stronger chess player and seeing what you could have done better. In this way you quickly learn from your mistakes and play a strong move the next game. Who said again "You learn twice as much from a lost game than from a won game"?