Before you do anything, refer to the rules and see what exactly is needed of you before joining the league. Last time, we had a few players quit after a few games and a few more became inactive a few weeks later. To ensure the best quality for all parties involved, it's best if you can decide whether or not you are dedicated to play at least once a week and then giving word if you want to join or not.
After you've joined the league, read the komi rules before playing your first game. These are important and they ensure balance amongst players.
After you play your game, one of the participants should edit the League standings. First, read the points system to figure out how many points the winner receives. Then go and edit their games played total, their win/loss total and their point total (losers point total stays the same). Afterwards, move the players into the appropriate places depending on their points (e.g. if Player A is in first with 5 points and Player B is in second with 4 points and Player B beats Player A, Player B's point total increases to 7 and he is moved above Player A). Afterwards fix the position number in the most left hand column and then update the players "rank". Remember, the winners total increases by one (1) and the losers total decreases by one (1).