My basic cleaning procedure requires some foaming bore cleaner (I use gunslick), Hoppe's #9, a bore snake (a rod with patches will also work but takes a little more effort), a spray can of Rem oil, a rag, a couple Q-tips, and a nylon AP brush (the toothbrush looking things at the gun store).
To get started, I point it in a safe direction and ensure it's unloaded, then I make sure it's unloaded again. With no ammunition in the area, I field strip the pistol and separate its components. As soon as it's field stripped, I fill the bore and chamber with the foaming bore cleaner and set it aside. With the nylon brush and Hoppe's #9 I'll scrub the carbon from the slide and frame, wiping off the loosened crud with my rag. The Q-tips get used in the same way, but primarily in the nooks and crannies I can't reach with the brush. Pay special attention to the slide rails, breech face (Especially under the extractor) and feed ramp. Then wipe the frame, slide and recoil spring down with the rag, removing any excess solvent, A quick spray throughout with the Rem Oil (heavy enough to make it wet, but not dripping) gets the lubricant where the gun needs it, and the excess gets lightly wiped off with the rag. By now the foaming bore cleaner has worked its' magic and I'll run the bore snake through the barrel once or twice (If you've done a lot of shooting or are using a rod and patches you may have to repeat the foaming and patches process). Then I give it a quick spray of Rem oil in each end of the barrel and run the bore snake through one more time. A little oil or gun grease goes on the barrel wear points and locking lugs, and it's time to reassemble and function check. That's all there is to it. It takes about 15-20 minutes for most semi auto pistols, maybe another 10 minutes for a rifle.
No, this doesn't get every molecule of copper out of the bore, or every atom of carbon out of the frame- but it isn't meant to. The purpose of this basic cleaning is to ensure reliable function the next time I need to use the firearm and prevent corrosion while it sits in the safe. The most common reason I see firearms not function correctly is lack of cleaning. This method is quick and easy and will help you spend less time cleaning and more time shooting!