I can't find anything in Ki Khanga about when or how to deal damage without a special Effect. The Combat section (KK 83) just says to look at the Action Resolution section for info on what happens when you Fail or Fumble, but that section (KK 79-82) doesn't say anything about what a Failure or a Fumble (or any other outcome) actually means: it looks like a purely narrative decision.
Neither can I find any examples that involve damaging attacks. The entry on Health (KK 16) says that Health is a buffer before I take "critical Conditions," but neither that section nor the Conditions section (KK 84-86) talk about how damage is inflicted nor how to determine which Conditions are imposed.
The weapons section is equally confusing; I'm guessing that the "Partial/Full/High" entries on the weapon tables are about damage, but that's just a guess and I don't know how it ties into Combat actions.
There's plenty about how to prevent damage, and how to heal damage and Conditions, but I'm still in the about determining when (and how much) damage is inflicted.