If you are talking about the cards in this game. Then when you have three of them, at the start of your turn, it will ask you if you want to trade them in. I think this only shows up if you have three that you can turn in.
Well, at the end of your PREVIOUS turn if you have taken over an enemy area (but not accomplished any objectives) you get a choice that pops up where you select the star card and it shows you if it had 1 or 2 stars on it.
By selecting the card at the end of your turn, after all of the other reinforcements are calculated, the star screen will pop up (so long as you have 2 or more stars) and show you how many stars it takes to trade in for how many armys, and then it will let you select the amount of stars you wish to trade in (if you have more than 2, you can always trade in less than your current maximum and save some for later).
HOWEVER, if you accomplished an objective the previous turn and instead chose to take the objective bonus, then you don't get to use stars for reinforcements on your next turn.
As it's almost always more beneficial to take a objective bonus, you might have selected one and thus made yourself ineligible for trading in stars for the next turn.
So... to sum it up... (for those aggravating people who type tl;dnr)
1. Take an opponent's country over to get a star card. 2. At the end of your turn, select the star card and see how many stars you got. If you select a objective bonus, then you have to wait another turn to get to trade in stars. 3. At the beginning of next turn, it will let you trade in your stars if you have more than 2.
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