You cast the instant or sorcery card as part of the resolution of this spell. It's cast from your opponent's library, not your hand. You choose modes, pay additional costs, choose targets, etc. for the spell as normal when casting it. Any X in the mana cost will be 0. Alternative costs can't be paid.

If you can't find an instant or sorcery card that can be legally cast, or choose not to find one, skip that part of the effect. Then the opponent shuffles his or her library.