Niv-Mizzet's genius and vanity reverberate throughout the mirrored halls of Nivix.

Nivix, Aerie of the Firemind

{T}: Add {C}.
{2}{U}{R}, {T}: Exile the top card of your library. Until your next turn, you may cast it if it's an instant or sorcery spell.

The List

Duel Decks: Izzet vs. Golgari

{T}: Add {1} to your mana pool.
{2}{U}{R}, {T}: Exile the top card of your library. Until your next turn, you may cast that card if it's an instant or sorcery.

Guildpact

{T}: Add {1} to your mana pool.
{2}{U}{R}, {T}: Remove the top card of your library from the game. Until your next turn, you may play that card if it's an instant or sorcery.

"Until your next turn" means the effect wears off as soon as your next turn starts, even before you untap. It's basically the same as "until the end of the turn of the player who immediately precedes you."

If you don't cast the card, it stays exiled.

The card is cast using all normal rules and restrictions for casting spells. Casting it means you'll have to pay its mana cost, and it will go to the graveyard after it resolves or is countered. The only thing that's different is you're casting it from the Exile zone.