The best way to understand the tennis rules is to watch them either on TV or live. A player needs to win 6 games to win a set, and then needs to win the best of five sets to win a match. In most cases, female players just need to win the best of three sets.
To win a game, you need to win three points, the first point is 15, second is 30 and the third is 40. If you both win three points, i.e. 40-all or deduce, you need to win 2 points in a row to win the game. So sometimes, it can take a while for a game to finish.
If you and your opponent both win 6 games within a set, you need play tie-break. The player who wins 7 points and has a margin of 2 points wins the set.