One handy thing I learned from my bike mechanic son is to take an old t-shirt or similar thing and tear off strips about 1-2 inches wide and about 12 inches long. (easier to use than a big rag or towel). Then slip the strip in between the rings on the cassette, and pulling back and forth gets out an amazing amount of stuff. Doing this occasionally makes it much less necesary to to the liquid cleaner thing very often. At that point, spraying the rags a little also helps. All this is easiest on a bike stand!
In really nasty cases, removing the chain and soaking in a big old coffee can before brushing is a lot nicer than doing it in dishpans or sinks!