Ask 10 people, get 10 different answers.
I like to use two products for cleaning and one for lubing.
Milcom MC25 Spray cleaner. Two blasts or so and wipe of floating/suspended gunk with a shop towel (SLIP makes a similar product, 725 Cleaner/Degreaser).
Next, soak carrier in SLIP 2000 Carbon Cutter. 10-15 minutes. This takes care of about 98% of the built up carbon, and unless you're pretty anal, you can declare victory at this stage. Otherwise do some light brushing to take care of any minute remaining crud. Follow with a quick wipe down.
Lastly, lube with a good CLP -- FP-10, SLIP 2000, the new Weapon Shield or just use a dedicated lube -- TW-25B, Eezox, whatever.
The main thing I've come to like about my approach is there's little work on my part; a spray, a quick wipe, a soak (during which time I tend to the upper/barrel and FCG), and a 2nd quick wipe down and then an application of lube. It's pretty simple.