Someone who is learning English asked me if there is a rule for using a K as opposed to a hard C. I wasn't sure, but I vaguely recall hearing there was one. Can anyone enlighten me?

Not sure what kind of rule you're looking for, but English orthographic c is 'hard' (i.e., a stop rather than a sibilant or fricative) before a, o, or u (mainly back vowels). It is 'soft' before e or i (or y) (mainly front vowels).

So, cat, caught, cot, coat, couch, and coot, but cedar, cilia, or cyan. But, ketamine, kit, or kyne. I'm sure some of the other folks will come up with some interesting exceptions.