We periodically get the official stats as published by the game developers via APIs.
The stats for each game are then processed according to the rules of the tournament. For example, you might get 20 points for a win, then 5 points for each kill,
These rules are different for various types of tournaments, as well as across different games. This all gets added up. Then your best games by the score are averaged or summed together to produce your final score.
Please be sure to review the Rules tab of each tournament to ensure you are playing the correct game mode for your scores to count and to see the number of matches that count toward your total score. While most tournaments calculate your score based on your best ten games, this may vary depending on the specific event or tournament.