Example #1:
Player A activates "Dark Hole."
Player B chains "Imperial Order."
Player A chains "Mystical Space Typhoon" from his/her hand. Also, you can chain or play a Quick-Play Spell Card from your hand during any Phase of your turn, even during your Battle Phase. Activating/chaining/playing Quick-Play Spell Cards from your hand, during your turn, is not limited to Main Phase 1 or 2 and can occur in the Draw, Standby, Battle, and End Phases. Of course, you cannot activate a Quick-Play Spell Card from your hand during your opponent's turn.
You can also Set a Quick-Play Spell Card during your Main Phase 1 or 2. Once you Set a Quick-Play Spell Card, you cannot activate it that turn (similar to a Trap Card) but can activate it on any subsequent turn. (This rule does not apply to normal Spell Cards; you may Set "Raigeki" during your turn and still activate it that same turn).