When this spell is cast, its "when you cast" ability triggers and goes on the stack on top of it.
As the triggered ability resolves, the active player gets the option to perform the action. If that player declines, the next player in turn order gets the option. As soon as any player performs the action, the spell is countered, but the remaining players still get the option. If all players decline, the spell remains on the stack.
A player can't choose to discard unless they actually have three cards in their hand.