How does +damage gear work?

The formula to calculate the +damage coefficient (what percent of the full damage bonus you get for each spell) is (cast time / 3.5).

• Direct damage spells - Shadow Bolt takes 3 seconds to cast (without talents), so it receives (3 / 3.5) = 86% of the damage bonus. If you had +100 damage gear, your Shadow Bolt (Rank 10) would hit for an average of 510 + 86 = 596 damage. Talents, buffs, and debuffs do not affect how the damage bonus is calculated, so Bane does not affect Shadow Bolt's damage bonus. As of patch 2.0.1, there is no longer a cap of 3.5 seconds max to determine how much bonus spells get. Soul Fire, for example, receives 6 sec / 3.5 = 1.71 = 171% of the damage bonus.
  
  
• Instant cast spells, such as Shadowburn are considered to have a minimum of 1.5 sec casting time. Example: Shadowburn would be (1.5 / 3.5) = 43% damage bonus.
  
  
• DoTs receive (duration / 15) of the damage bonus, spread over each of its ticks. Example: "DoT X" lasts for 18 seconds, so it receives 18 / 15 = 1.2 = 120% of the damage bonus. Since DoT X is spread over six ticks, each tick receives 120% / 6 = 20% of the damage bonus. (Note: Corruption, Curse of Agony, and Curse of Doom were nerfed in patch 2.0.3 (1/9/07) with hardcoded coefficients, so that they no longer observe the above rule for DoTs)
  
  
• Hybrid spells that both deal damage and heal the caster only receive 50% of what they "should". This is because although you are damaging for 50% more, you are also healing for 50% more. The health spread between you and your opponent therefore increases by 100% of the damage bonus. Drain Life and Siphon Life are both DoTs that are affected this way. Death Coil, on the other hand, is not a DoT but an instant cast spell, so it receives 43% (as an instant cast spell) divided by 2 = 21%.
  
  
• AoE spells are calculated like direct damage spells, except they only receive 1/3 or 33% of what they "should", spread over each tick. Rain of Fire, for, example is 8 sec / 3.5 = 2.29; 2.29 * 1/3 = 76%.
  
  
• Life Tap - Life Tap receives 80% of your bonus spell damage effects. Talents and items can further modify those values. Rank 1 and 2 receive reduced effect (38% and 68% respectively). Life Tap benefits from +damage/+shadow gear and buffs that increase your shadow damage by a fixed amount (ie ToEP, shadow power potions, flask of supreme power, etc.). It does not benefit from percent-based buffs and talents such as DS, SM, and Power Infusion. Improved Life Tap is calculated after +damage gear. To calculate your Life Taps, use the following math:
  
  Without Improved Life Tap: x = [420 + (+dmg * .8)]
  With Improved Life Tap: (x * 1.20) mana for x health
  

The damage bonus received by each warlock spell is as follows:

• Affliction
  Corruption - 93%
  Curse of Agony - 120%
  Curse of Doom - 200%
  Dark Pact - 96%
  Death Coil - 21%
  Drain Life - 71.5%
  Drain Soul - 215%
  Life Tap - 80%
  Siphon Life - 100%
  Unstable Affliction - 120%
  
  
• Destruction
  Conflagrate - 43%
  Hellfire - 141%
  Immolate* - 20% direct damage, 65% spread over the DoT
  Rain of Fire - 76%
  Searing Pain - 43%
  Shadow Bolt - 86%
  Shadowburn - 43%
  Shadowfury - 14%
  Soul Fire - 171%
  

*Immolate is calculated this way:

Math
Immolate (Rank 7) - Burns the enemy for 279 damage and additional 510 damage over 15 seconds. 2 sec cast.

• Direct damage component:
  (2 / 3.5) = 57.14%
  [279 / (279 + 510)] = 35% of Immolate's total damage dealt
  .57 * .35 = 20% total damage bonus
  
  
• DoT component:
  100% - 35% = 65% of Immolate's total damage dealt, and since DoTs get 100% of the damage bonus, the DoT part of Immolate gets the full 65%.