If you want to leave the parts on the bike, then I suggest getting a pourable citrus degreaser (Finish Line seems stronger than Pedros, that's what I use), and using a cheap 2" paintbrush. Pour a small amount of degreaser into a can, dip the brush, spin your rear wheel backwards and swab the cassette cogs as they turn (and you can get the chain while you're at it). Keep an eye on where the degreaser's running off to and try not to let it near the bearing areas.

After a minute or two, rinse away the citrus degreaser with hot sudsy water, dry the chain as much as possible, and relubricate it promptly. Rinsing the citrus degreaser away with Simple Green Foaming Degreaser first will get stuff even cleaner, the two degreasers annihilate eachother and the grime comes pouring off in the process. But if you're working on a daily-driver bike that's just going to get dirty again, don't get too carried away trying to make it spotless.