3 to 9 casings can be found on the dead body of an enemy that was wielding a varmint rifle or a service rifle at the time of their death.
When you fire a weapon chambered in the 5.56mm round, there is a 20% chance you'll get a casing.
You'll get 25 5.56mm casings if you buy a 5.56mm case box.
Occasionally some traveling merchants will "sell" 5.56mm casings (among many other calibers), but they will always be for free. Likewise, if you try and sell casings to a merchant, you will not yield any money.