Originally Posted by Kimmo

How's WD40 and a rag grab ya?

If you don't want to use WD40, a dry rag often works well, but for caked-on dirt you can just dampen it with water. Should work for 99% of grime, but might take a bit of elbow grease.

You can do a perfectly good job, but full disassembly is a must to do a complete one.

Chain cleaning? That's a whole other ball game. IMO the best way would be wrapping around a bunch of jockey wheels submerged in solvent with bubbles.