You select the card you are activating in your opponent’s Graveyard when you activate “Double Spell”. “Double Spell” can then be chained to after you announce your selection.
The selected card itself CANNOT be chained to as you are in resolution of the chain at that point.
If the selected Spell Card is Ritual, Normal, or Quick-Play (except for “Swords of Revealing Light”), it remains in your opponent’s Graveyard and is not placed on the field, so you only need 1 vacant Spell & Trap Card Zone spot (for “Double Spell” itself) to activate “Double Spell”.
If you activate “Double Spell” and select a Continuous, Field, or Equip Spell Card, or “Swords of Revealing Light”, you place the selected Spell Card in your Spell & Trap Card Zone, so you need 2 vacant Spell & Trap Card Zone spots (1 for “Double Spell”, 1 for the selected card). The Continuous/Field/Equip/”Swords of Revealing Light” Spell Card then remains on the field as normal.
The player who activates “Double Spell” pays any costs for the selected Spell Card (for “Delinquent Duo”, “Tribute to the Doomed”, etc.).
You cannot select a Spell Card with “Double Spell” that cannot be activated, such as an Equip Spell Card when no monsters are on the field.
You cannot use “Double Spell” while “Necrovalley” is in effect.
Netrep Q&As:
Q: When activating “Double Spell”, will cards like “Skilled White Magician” or “Skilled Dark Magician” receive 1 or 2 Spell Counters?
A: Only 1 Spell Counter. You get 1 Spell Counter for “Double Spell,” but not one for the targeted Spell Card because it is never activated. (The targeted Spell Card does its thing during the resolution of “Double Spell.”) Curtis Schultz, 04/07/2004