For starters, you have a many to many relationship between teams and games. A team will play many games and any game is played by two teams.
Start with these relationships:
Teams::__pkTeamID = Team_Game::_fkTeamID
Games::__pkGameID = Team_Game::_fkGameID
You can place a portal to Team_Game on the Teams layout to list and select a Games record for each given Teams record. Fields from Games can be included in the Portal to show additional info about each selected Games record and the _fkGameID field can be set up with a value list for selecting Games records by their ID field.
With that set up, the season, date, location, league/nonleague game status type data is entered in Games. The final scores and possibly a win/loss field would be kept in Team_Game.
And the data in Team_Game can be set up in a number of ways to show league standings for a given team in a given season.