You may register for a league game one of two ways. Click a league game from the actual league game lobby then click register for this league. Once registered you may join any registering game for that league.
For some joining through the game lobby does not work well, those may join by clicking Resources top of the lobby and choosing League schedule from the drop down menu. Choose the league you want to join from the list and click on the name of the league you want to register for, then register from the page that pops up.