Whenever an opponent casts their first spell each turn, that player exiles the top card of their library. If it's a nonland card, you may cast it without paying its mana cost.
7/13/2016 If you cast the exiled card, you do so as part of the resolution of Mind’s Dilation’s ability. You can’t wait to cast it later in the turn. Timing permissions based on the card’s type are ignored, but other restrictions (such as “Cast [this card] only during combat”) are not.
7/13/2016 If you cast a card “without paying its mana cost,” you can’t choose to cast it for any alternative costs, such as emerge costs. You can, however, pay additional costs, such as escalate costs. If the card has any mandatory additional costs, you must pay those.
7/13/2016 If the card has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
7/13/2016 If you cast the card this way, it will resolve before the spell that caused Mind’s Dilation’s ability to trigger.
7/13/2016 If you cast an instant or sorcery card this way, it goes to its owner’s graveyard as normal. It doesn’t return to exile.
7/13/2016 If you don’t cast the card, perhaps because you choose not to or because it’s a land card, it remains exiled.