If a spell has both an additional cost and a cost reduction, which is applied first when calculating the total cost?

When you cast a spell, the total cost is assembled in a specific order defined by CR 601.2f. First, you start with the spell's mana cost (or an alternative cost if one is being used). Second, any additional costs are added on top of that base. Third, cost reductions and other cost-modification effects are applied to bring the total down. Finally, you pay whatever remains.

Importantly, the order in which you calculate doesn't usually change the end result mathematically, but it matters because cost reductions can never reduce the cost below zero mana of any type (CR 601.2f), and they apply after additional costs have already been tacked on. This means a cost reduction can offset an additional cost, which is intentional and works as expected.

For example, suppose you cast Spectral Sailor (normally {U}) but it has an additional cost of {2} imposed by an effect, making the assembled cost {2}{U}. If you then have an effect that reduces spell costs by {2}, that reduction applies afterward, bringing your final payment back down to just {U}.

One practical note: if multiple cost reductions apply, they are all applied in this third step, in any order the casting player chooses (CR 601.2f), though again the math is typically the same regardless of order. Cost reductions cannot reduce the colored mana requirements of a cost, only generic mana, unless specifically stated otherwise (CR 601.2f).

So the structured sequence is: (1) base cost, (2) additional costs added, (3) reductions applied, (4) pay the final total. This order is mandatory and codified in the rules.