So I know how to calculate spell DC (8 + proficiency + modifier) and spell attack rolls (1d20 + proficiency + modifier), but I am not clear on spell damage.
Namely, do you add your spell modifier (e.g. int for wizards) to spell damage?
For example, burning hands does 3d6 fire damage or half as much if the opponent succeeds on a dex save.
If you have a Wizard with 16 Int casting it with a 1st-level spell slot, does the spell do 3d6 (or half) damage, or 3d6+3?
No
A spell does the damage it says it does. In the case of Burning Hands, it says it does 3d6, so it does 3d6.
There are a few exceptions to this: the school of Evocation for Wizards allows you to add your spellcasting modifier to the damage of evocation spells, and certain Cleric domains allow you to add your spellcasting modifier to the damage dealt by cantrips. There is an invocation that allows a Warlock to add their spellcasting modifier to the damage dealt by Eldritch Blast. The Dragonblood Sorcerer can add their spellcasting modifier to spells that deal elemental damage matching their bloodline type.
Outside of these, though, the only reason a spell would add your spellcasting modifier to damage is if it says that it does. I’m not aware of any spells that currently do this.