The best time to improve your players is while they're either injured or inactive. In that way, once they're back in the lineup, their performance will be much higher.
Your winning streak in the "Play Game" section is very important since it can help you earn a great amount of income. If you're not sure if you can beat an opponent, you should either choose another opponent or refresh the opponent list. Your winning streak is everything.
The special competitions such as the Playoffs or the Superbowl will give your players even more points than usual. Signing the players who participate in these competitions will give you the chance to play against opponents with even higher values.
You can earn a lot of rewards by playing the tournaments, but there are very exclusive power ups that you can only get in these competitions.