Oracle Text

Counter target spell. If the spell is countered this way, exile it with three time counters on it instead of putting it into its owner's graveyard. If it doesn't have suspend, it gains suspend. (At the beginning of its owner's upkeep, remove a time counter from that card. When the last is removed, the player plays it without paying its mana cost. If it's a creature, it has haste.)

Card Rulings

5/1/2007 When the last time counter is removed from the exiled card, it’s cast as a completely new spell. Modes and targets are chosen again. If the spell has any additional costs, they must be paid again. If they can’t be, the spell can’t be cast and stays exiled.
5/1/2007 If the spell targeted by Delay was cast with flashback, Delay’s effect will exile it, not the flashback effect. The card will get time counters and gain suspend (if it didn’t already have suspend).