Use some type of solvent for the barrel (Hoppe's, MPro7, etc.). Run a wet patch through the barrel, let sit for a few minutes, run a wet brush through it a dozen times or two. Follow with wet and dry patches on a jag until the dry patches come out white. Visually inspect barrel to make sure it's clean. Put one patch w/ CLP through the barrel, followed by a dry patch.
Use CLP on everything else. I spray some on an old toothbrush and go to town on everything inside the slide and frame, paying particular attention to the rails, breech face, and extractor. Wipe off all excess CLP w/ patches and Q-tips. Your pistol's stainless, so it should be easy to see where the grime's hiding. Toothpicks are good non-marring tools for scraping out tough to reach crevices.
When I'm scrubbing the breech face, I like to tilt the slide downwards so CLP doesn't get into the little hole where the firing pin comes out. Oil in there attracts dirt, and it might get the pin stuck after a long while. Too much oil anywhere will do that. That's why it's important to wipe off all excess oil. I actually believe it's unnecessary to add any further oil to the rails after I've just cleaned them w/ CLP.
Every once in a while (maybe once a year), completely take down the pistol and clean everything (like the firing pin area). If you're not sure how, bring it to a gunsmith. Or you can kinda get by w/ spraying GunScrubber throughout and relubing afterwards w/ CLP. Detail stripping is better, though, and you should learn how to anyways.
Generally speaking, most gunnies tend to over-clean their guns. Some believe more wear is attributed to excessive cleaning than actual use of the gun. As long as you're not shooting ancient corrosive ammo, you can prolly get away w/ not cleaning your pistol after EVERY range session. If it's a working gun (as in CCW, HD, etc.), then DO clean it every time.
Hope that helps.