How do you clean a grinder?

I have a DuraCasa manual grinder with ceramic burrs. How should one go about cleaning this?

For basic cleaning I would take it apart and brush out any excess grinds that are sticking or matting up in the burr grooves. Though given that the burrs are ceramic, dunking them in water for a deeper cleaning could also be done.

Run Grindz or minute rice through it.

I'd go with hot, soapy water and a very good rinse. There is nothing about that grinder that can't take water. If you are worried about soap residue, maybe give it another rinse with dilute vinegar, followed by more hot water.