Wellll... not so much saving, but getting the most out of your resources. Early on (really until you are done building) the facilities should be a priority along with good players. So you need to save up enough for the next facility (stadiums get very expensive) as well as having enough to sign new guys and renew contracts. I try to buy later in the Season so no bidding war/high price many Token players.

But too, you want to buy the most expensive players as usually they are faster trainers and will last longer in your team, saving money by not having to buy a new guy next season. Try to build toward having the starters be the best you can afford, and go cheaper with the bench... and eventually they will rotate out as the starters age/lose stars.