The exiled card is played using the normal timing rules for its card type, as well as any other applicable restrictions such as “Cast [this card] only during combat.” For example, you can’t play the card during an opponent’s turn unless it’s an instant or has flash. Similarly, if the exiled card is a land, you can’t play it if you’ve already played a land that turn. If it’s a nonland card, you’ll have to pay its mana cost. The only thing that’s different is you’re playing it from the Exile zone.