Barrel
1. Soak one patch in Break-Free CLP (though Hoppes #9 can work too, I just prefer CLP). Pass through the barrel once in each direction, then discard.
2. Take bronze bristle brush, run through barrel one cycle for every 10 rounds fires (200 rounds = 20 forward and back brush strokes).
3. Soak patch in CLP, run through barrel once in each direction, then discard.
4. Alternate wet/dry patches until they come out mostly clean.
5. To finish up, apply CLP (or quality gun lubricating oil) to patch, pass through barrel once in each direction, discard.
6. Pass dry patch through barrel once to absorb excess oil. This allows a very thin film to remain, protecting the bore from rust.
7. Wipe down outside of barrel with oiled patch, then wipe dry.
Alternative Barrel Cleaning
1. Apply CLP to pre-brush area of a boresnake.
2. Pass boresnake through barrel twice.
3. Wipe outside of barrel with oiled patch, wipe dry.
Action
1. Apply CLP to patch, wipe liberally removing most of the gun.
2. Wipe dry.
3. Apply oiled patches/q-tips to various parts until they come out mostly clean.
4. Wipe dry.
5. Apply small drops of oil to necessary lubrication points (see gun's manual), and any points where metal is "shiny" from wear.
6. Wipe up excess oil, leaving only a thin film.
7. Wipe down external parts of the action and gun with an oiled patch, then wipe dry.
One should wipe down springs and other components with an oiled patch, but wipe them dry. Excess oil (more than a thin film) holds airborne gunk and builds it into a gritty sludge, which may cause issues. Most parts in a gun don't require lubrication, though slide rails in pistols do require a bit. Just keep parts clean, wipe with an oiled patch, and wipe dry.
Grease is generally unnecessary unless called for on your gun (such as the working parts of an M1 Garand, which will sling oil all over the place, such as into the shooter's face). Otherwise, the heavier grease can slow down the action by a small amount, which may lead to issues. It also exhibits the same gunk-holding ability of wet oil.
Guns usually require no more than a few drops of oil in their working parts -- if I recall correctly, the Glock pistol requires no more than 5 drops of oil (with the excess wiped away) to function properly.
Guns don't need to be perfectly shiny and clean to operate. In fact, over-cleaning can cause premature wear of the gun. Make sure the parts are free from crud, and the bore doesn't have any visible fouling, oil the parts that need oiling, and you'll be set. There's no real reason to keep guns perfectly clean in all respects.