Anyone can play a card whenever the card allows it. Playing a card means using a power on that card by performing an action with that card that is specified by the card itself. You must do everything the power says when possible. When you play a boon has several powers, you must choose only one of them.
If a card in your hand does not specify when it can be played, you can generally play it anytime you can play cards, with the exception that during an encounter you may perform only specific actions at specific times (see the Encountering a Card section for more details).