The little strips of cloth are what I call 'gear floss'. Old towels, t-shirts, anything you can tear into strips works. Then after you run the chain thru a chain cleaner, you take the 'floss' and run it between the cogs (rear gears/cassette) as you do floss between your teeth. Works great.
The Favor polish is a cheap-ass Pledge knock off. After the bike is clean, and you have the wheels off, spray the frame and fork with the polish. Hold a rag/cloth over the gears, brakes pads and anything you wouldn't wants waxy polish to get on. Let the polish sit for only a couple minutes then wipe it off with a clean cotton cloth. The polish gives a nice shine to any parts of the bike that are painted and/or clear coated--it also makes mud or other grime wipe off easier later on.