What to use to clean your chain (and cogs)?
A degreaser, whether aerosol or not, is an excellent way to remove grease from the chain. 

http://www.finishlineusa.com/products/citrus-cleaner.htm

http://www.finishlineusa.com/products/speed-clean.htm

The degreaser will reduce the amount of elbow grease required but be careful and use a set of nitrile gloves to protect your hands. 

My simple chain cleaning method is as follows:

Shift into the big ring and little cog, wet the rag with the degreaser

Grip the chain (lower portion, going from big ring to the derailleur) with the rag, focusing on holding firmly onto the outer plates.

Turn the crank putting the chain through the rag. Readjust as necessary as you remove grease and grime from the chain (ie. don't keep rewiping schmutz back onto the chain).

When sufficiently clean, remove the rear wheel from the bike and place it between yourself and a wall (ie. tyre against your stomach/tyre against the wall keeping the wheel propped between yourself and the wall) over a garbage can. 

Using a thin screwdriver or a cleaning tool ( http://www.parktool.com/products/detail.asp?cat=4&amp;item=GSC-1 ) clean the grass and grease build up from between the cogs of the cassette/freewheel. Lightly apply degreaser to the brush portion of the tool and scrub at the cogs to free up the grease/grime.

Using a rag, with degreaser on it, insert the edge of the rag between the cogs and 'saw' back and forth with your hands thus spinning the cassette and fully wiping the whole cog. I typically move from top to bottom of the cassette (keep the grime flowing downwards). 

Wipe down cassette, hub and any spokes/rim that could have been contaminated. Reinstall the wheel in the bike and one last time wipe down the chain with the degreaser rag. 

And typically ... that method suffices for cleaning any of my bikes. The one caveat is that I typically don't let the chain get grease/grime covered and thus this takes about 3-5 minutes max and works really well. The worse your chain, the more you have to do. 

You might want to look at your derailleur pulley wheels and using a flat edge against the pulleys as you spin the crank, remove the grease rings from the pulleys.

You might want to pre scrub the chain (similar to how you did the cassette) to loosen the grease/grime on the chain. A tooth brush w/ degreaser or the GSC-1 mentioned above would be sufficient.

Andddd... that's about all I've got for now. There are a plethora of other methods using chain cleaning tools, removal and soaking of the chain and nastier solvents but for the majority this method seems to work fairly well.