The chainrings get Simple Green on them as the Park Tool chain cleaner gets the chain soaked and clean.
I use a rag to shield the rear wheel/tire from excess SG dripping off the chain and derailleur pulleys. That rag gets fairly well soaked and I use it to wipe down the chainrings, pulleys/cage assembly and finally to floss the cassette gears.
Chains and gears on a bike are the perfect representation of an exposed roller chain driveline...and all the dirty drawbacks that go with such!
Chains and gears are supposed to be dirty.
I never try to get my driveline 'you-can-eat-off-it' clean. My intent is to flush as much of the abrasive dirt and grit off as possible. The minute you apply new lubricant and go out for that first 20-miler the old stuff that invariably is still under the rollers comes flushing out black. Or you pick up a new coating of horse ****, road grit, dust, car rust, etc. And it is all busy getting dirty looking again.
For those that clean between 'cleanings' with just an old sock or rag and re-lube, the driveline is never operating room clean. But neither is it a real ***** to get it back to 'that looks damned good!'. The folks that clean once a 3000-mile summer and just keep re-applying more lube as needed...they are the ones with a real mess on their hands...and shirt...and floor...
There's a happy medium between the OCD folks that only use operating room/clean room standards, sterile dry lube and lint-free rags made from virgin sheep and the crud-caked components like most of the local club members seem to have three weeks after their annual tune-up at the LBS that lasts until the next appointment with the (deservedly) depressed mechanic.
Only you and you mileage/road conditions can determine a schedule/lubricants that keeps your chain and cassette alive the longest and we can all be proud of our right-inside-calf black stripe jobs every now and again.
Lately, I've been pre-lubing (prior to applying the oil) my cleaned chains with aerosol chain lube from Liquid Wrench:
http://www.liquidwrench.com/products/
It foams on, penetrates into the pins/rollers and dries to a clingy, tacky, waxy feel. I like it. $2/can at Menards and also available in liquid, bottle format (but I do so enjoy killing the ozone layer and pissing off the tree huggers).
Despite alien ranting on about how poor the human is at observing and quantifying 'stuff', I will ask you all...is there ANYTHING in cycling that feels smoother and faster than a racing bike that just had a thorough driveline cleaning and lube?!?!