I just back pedal while holding rag around the chain to wipe it down. Then I back pedal and apply plenty of SAE 90 oil, and then I back pedal again with a clean rag to wipe off excess. Then I wipe down the chain rings and clean the cassette by edging a rag in between the sprockets.

I do this once every week to two weeks, but I also do it after a rain ride (after cleaning the whole bike with a quick spray and wipe down.)

I use SAE 90 mostly out of habit from my motorsickle daze.