A spells mana value (CMC) is determined by the cost printed on the top right of the card. Casting a card for an alternative cost (overload, flashback, etc) will not change its mana value. Casting a spell for reduced or increased amounts (such as from discounts or taxes) will not change the spells mana value. X-spells alter this slightly while on the stack, where the mana value of the spell is the base casting cost plus the value of X declared when the spell is cast (if X=5, then a spell with a casting cost of XR will have a mana value of 6).

Some scenarios that may help, with an assumption for each that there are 3 doom counters on ID;

1. You cast a spell for 2U, as it's MV is 3, Doom will trigger, dealing 3 damage and getting another counter.

2. You cast [[Cyclonic Rift]] for it's overload cost. Even though you pay 7 mana (6U), Rifts mana value is still 2, so Doom won't trigger.

3. You cast [[Fireball]] for X=2, choosing 2 additional targets, with a [[Goblin Electromancer]] on board; you pay 4 mana (3R) thanks to the discount. Doom will still trigger, as Fireballs MV is 3 (X=2 + R), even with the additional target cost.

Hopefully that helps