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If the spell is modal, the player announces the mode choice (see rule 700.2). If the player wishes to splice any cards onto the spell (see rule 702.47), they reveal those cards in their hand. If the spell has alternative or additional costs that will be paid as it’s being cast such as buyback or kicker costs (see rules 118.8 and 118.9), the player announces their intentions to pay any or all of those costs (see rule 601.2f). A player can’t apply two alternative methods of casting or two alternative costs to a single spell. If the spell has a variable cost that will be paid as it’s being cast (such as an {X} in its mana cost; see rule 107.3), the player announces the value of that variable. If the value of that variable is defined in the text of the spell by a choice that player would make later in the announcement or resolution of the spell, that player makes that choice at this time instead of that later time. If a cost that will be paid as the spell is being cast includes hybrid mana symbols, the player announces the nonhybrid equivalent cost they intend to pay. If a cost that will be paid as the spell is being cast includes Phyrexian mana symbols, the player announces whether they intend to pay 2 life or a corresponding colored mana cost for each of those symbols. Previously made choices (such as choosing to cast a spell with flashback from a graveyard or choosing to cast a creature with morph face down) may restrict the player’s options when making these choices.

Buyback

Buyback appears on some instants and sorceries. It represents two static abilities that function while the spell is on the stack. “Buyback [cost]” means “You may pay an additional [cost] as you cast this spell” and “If the buyback cost was paid, put this spell into its owner’s hand instead of into that player’s graveyard as it resolves.” Paying a spell’s buyback cost follows the rules for paying additional costs in rules 601.2b and 601.2f–h.

If the spell that's copied has an X whose value was determined as it was cast, the copy will have the same value of X.

The copy will have the same targets as the spell it's copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. If, for one of the targets, you can't choose a new legal target, then it remains unchanged (even if the current target is illegal).

If the spell that's copied is modal (that is, it says "Choose one —" or the like), the copy will have the same mode. A different mode can't be chosen.

If the spell has damage divided as it was cast, the division can't be changed, although the targets receiving that damage still can. The same is true of spells that distribute counters.

You can't choose to pay any alternative or additional costs for the copy. However, effects based on any alternative or additional costs that were paid for the original spell are copied as though those same costs were paid for the copy.

The copy is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger. The copy will resolve before the original spell does.

Reiterate can copy any instant or sorcery spell, not just one with targets.