Did Cristiano Ronaldo become a world class fotball player in a month?
You improve after every game, but you improve in decimals. That is, your player gets for example 0.15 points of Top Speed after every match, and once they add up to 1.0 you get 1 point in Top Speed. Playing matches increases your improvement rate, and bigger clubs (more training points) increase the rate as well. It's better in regards to personal improvement to play all matches at a weaker club than being on the bench/reserve squad of a top club. That being said, your player will become insanely "overpowered" in a few seasons regardless of your choices, unless you're really REALLY poor at this game.
Once you can afford the +5 training thingy to one of your abilities, you can pretty much erase any shortcomings the game intended to give you at the beginning, if the shortcoming is Top Speed, for example, you can further enhance that ability easily with a +5 pair of boots. If you note which boots you prefer, and use that knowledge smart during player generation, you'll basically start out with a star player who'll become too good to be true during the very first season.
By "misusing" the above mentioned strategy I've managed to score over 100 goals in my first season as a midfielder. I've had to implement personal rules to make the game interesting again, like never going past 84 in any ability and I'm using a save editor to keep my abilities low enough. This also helps the game to remain fairly decent, as the AI doesn't get overly insane because of my players abilities. Once one of your abilities surpass 94 the friendly AI of the game becomes mentally deranged and the opponents are on steroids. This includes form arrow and Supersub card boosts, so basically going past 84-86 (depending on ability) not only makes your player too good, it also ruins the game.
