How do I clean a suppressor, and how often?

Depends entirely on the host. Rimfire cans get filthy fast and are usually built to come apart for cleaning — plan on servicing a .22 can every few hundred rounds or it'll start to seize. Centerfire rifle cans are largely self-cleaning; the heat and pressure burn off most fouling, and many are fully sealed and not meant to be opened at all — forcing apart a sealed welded can will ruin it. For pistol cans, follow the maker's guidance. Bottom line: read your manufacturer's manual first, and never disassemble a can that wasn't designed for it.