For most people doing this at home the easiest would be something like this:

Get some good degreaser. I really like the Pedro's stuff, it's thick, stays on, and cleans well.
Put some in a cut down water bottle and use a 1" brush to paint it on the cogs, chain, and rings. You can definitely slop it on the derailleurs too.
I have a toilet cleaning brush that works well on the cogs and chainrings, I use a cheap car wash sponge w/ soapy water (I use Dawn) for doing the chain. Wrap the sponge around the chain and back pedal. Rinse w/ your hose or whatever. Dry. Lube. Don't let it get dirty again. The more you clean the less time it takes.

And of course...this post should be in 'bicycle mechanics' not GD.