There are those who love to brag as to how long their favorite "brand x" pistol went between cleanings. What I rarely hear them brag about is the time it takes to eventually clean up the gun after these marathon sessions. This may be great for gun demo's, or bragging rights, it's horrible treatment for a tool that's supposed to keep you alive when you need it to defend yourself.
While some like to use all in one lube/cleaners, you sometimes need a specific copper remover or cleaner for your weapon. I like Hoppe's #9 or Gun Scrubber for a heavily dirty barrel or to remove lead from my revolver. If the gun has old style bluing, I like to check the cleaner first on a hidden area to make sure it won't damage the finish.
Beware that if the cleaning product you intend to use says "rust remover" on it, bluing is a slow rust process and will not survive even a dab of this cleaner.
I field strip the gun (after clearing it, of course) and clean/scrub the barrel, slide, and inside the frame. I take care to remove any carbon, lead, fouling, and whatever else is there, with a spray, brush, Q-Tip, rag, or some of the other things I will share in the tips below. Once these are cleaned I apply oil to any place I have metal to metal contact. This usually means the rails (both slide and frame), barrel, and if it has one, the barrel bushing.
Once it's all put back together I function test it. I take an EMPTY magazine and place it in the gun, and pull back the slide, and see if the slide lock works. Then, I eject the magazine, and rack the slide a few times. I then place a pencil, eraser side first, in the barrel, and pull the trigger. If the pencil shoots up, the firing pin / trigger system is working. I then rack the slide and verify the hammer/trigger reset. Once it all checks out, you're good to go.
Revolvers, especially stainless ones, are a bear when it comes to cleaning. The lead and fouling that accumulates in rings around the face of the cylinder are a real pain to get off, and take considerable time, solvent, and elbow grease from my experience. A good solvent such as Hoppe's #9 and a bronze brush is the best tool I've found for this job. Be careful with steel brushes they can damage many types of finishes.
The cylinder face and top strap on a revolver are easy to overlook, but these are crucial areas to really get clean. If you don't use a bronze brush to scrub, scrub, scrub all of the black carbon deposits away, these will be compounded the next time you shoot your gun.
Generally I don't take either a pistol or revolver beyond the level of field stripping for a good cleaning. But outside of periodic inspection, again, I tend to spray Rem-Oil through the action and let it drip out the other side. Rem-Oil is your friend and I use it for everything.
Cleaning the barrel may seem like a no-brainer to you, but there is an important consideration you should be careful of. The crown of the barrel effects accuracy more than anything else on the gun. If you nick the inside of the barrel end with a steel cleaning rod, it can seriously effect accuracy. The brass rods you get in a cleaning kit aren't an issue. Brass is softer than steel so can't harm it. But some of the high end cleaning rods are steel, and with many you have to pay extra to get the brass sleeve that protects the bore. This is a very important addition to any steel cleaning rod. These days there are great fiberglass rods as well and I suggest them regardless.
On an auto-pistol, where you are taking the barrel out of the gun before cleaning it, clean it from the back, and use your toothbrush or other hard bristle brush on the feed ramp to get it nice and shiny. Crud can build up on it and this is a primary cause of failures to feed.