I use WD40 chain cleaner, with half a milk carton underneath to catch drips and a bit of card tucked between the chain and the wheel to act as a chute for any that misses the chain so that it all goes into the carton. Then once the chain has had a good spray, you can use a brush (dipping it in the excess chain cleaner caught in the milk carton) on any nasty bits. Then dry the worst off with a dishcloth (doesn't leave fibers all over it like a towel can) and leave it for a bit to completely dry. Then blast it with WD40 chain lube, again using card to sheild the wheel. I hoard old ceral boxes for this; if you rip off one of the top flaps, the adjoining face, the adjoining bottom flap, and one of the sides, it stays fairly rigid but also fits nicely around the chain and swingarm. And any runoff catches in what's left of the bottom of the box, so no cleanup required.