Have 2 tables, Team and Game, where Team has a team name, and a team ID, and game has 2 team IDs (team 1 and team 2) and the score of the game. Then, you have foreign keys (for integrity) between the Game and Team tables. This will reflect who played who and what the score was with a minimal schema and a very simple structure.
Team
|-------------------------|
| Primary (int)| id |
| (chr)| name |
|-------------------------|
Game
|-------------------------|
| Primary (int)| team1 |
| Primary (int)| team2 |
| (int)| score1 |
| (int)| score2 |
|-------------------------|
So, some sample data would look like:
Team
|------------------|
| id | name |
|------------------|
| 1 | Blue Devils |
| 2 | Cardinals |
| 3 | Fish |
| 4 | Lemmings |
|------------------|
Game
|---------------------------------|
| team1 | team2 | score1 | score2 |
|---------------------------------|
| 1 | 2 | 7 | 8 |
| 1 | 4 | 2 | 25 |
| 2 | 3 | 8 | 2 |
| 3 | 4 | 17 | 18 |
|---------------------------------|
This data indicates that team 1 (Blue Devils) played team 2 (Cardinals) with a score of 7 to 8. The rest of the data is similar.
If you do not need to track the team names, you can leave that field out, but this is often useful information.
So, with this schema, you would get the scores for a particular team with a query like
SELECT * FROM Game g
INNER JOIN Team t on t.team1 = g.id
You could then also add additional information if you need to, like when the game took place (date), and any other information, such as other statistics about the game or team.