This is how I do it.
Kerosene! Nothing works better. Diesel fuel may be cheaper and/or easier to get and its pretty much the same thing with taxes. Kerosene is also good for cleaning road grime off your wheels.
Soak the chain with kerosene. I use an acid brush for this. Cut a terrycloth towel into small pieces and wipe. When the towel gets loaded throw it away and get a clean piece. Repeat until its clean wipe it down with a dry towel and oil the chain. This is much easier to do with the chain guard removed.
I don't like brushes because they splatter oil and dirt all over. Maybe I just to clumsy. Terrycloth will get into the corners just fine. Don't use a new towel unless your into lint.
I also suggest the Nitrile gloves:
http://tinyurl.com/a6pcm This is dirty work.