Field Strip the Rifle
Dismantle the firearm. Read the manual to the firearm on how to do this. On bolt-action rifles, it is usually only a matter of releasing the bolt. On auto-loading rifles, the tear-down will be more complex.
Identify the parts you are cleaning. The two primary areas that will require cleaning are the barrel and the receiver and action.
The barrel is the key factor attributing to the accuracy of the rifle. Be cautious with the muzzle-end of the barrel and the beginning of the rifling (inside the barrel), as these are the two most important things to affect accuracy and can easily affect it adversely, if damaged.
Receiver and action is the bolt, chamber, and trigger assembly. The bolt holds the ammunition in the chamber and the trigger assembly initiates the process which makes the firearm go boom. This area primarily affects reliability and ease of operation, but can also reduce accuracy if poorly maintained. For most rifles, the stock and receiver are one unit, and cannot be dismantled without tools.
Clean the Bolt and Chamber
Wipe down all components using some paper towel (or cloth, but this is less important to be lint-free).
Remove as much of the thick, caked-on carbon buildup created by the friction of use. Also wipe off any old oil and all unburnt powder buildup.
Be sure to wipe the inside of the magazine well (if available), the ejector, and the area around the chamber. You will find certain areas turn the paper towel black (clean these areas more).
On this step, precision is not required; wipe it quickly.
Spray solvent (preferably designed to be safe to continually contact your skin, like M-Pro 7) on all possibly dirty components.
Many rifle manufacturers design components (even polymer and the stock) to be safely used with any solvent, but be sure there aren’t types of solvents the manufacturer warns against.
A liberal amount of solvent is better than not enough.
Let the solvent sit for a couple minutes. Make sure any area with dirt, carbon buildup, or unburnt powder has a healthy amount of solvent on it, soaking in.
Scrub the whole gun with a brush (no metal bristles — like a toothbrush). This works in the solvent and loosens up the buildup on the gun. Try to get into all the nooks and crannies.
On a bolt-action rifle, be sure to scrub all nooks and crannies of the bolt (when it is removed from the receiver).
On a gas-operated rifle, special care may be required while cleaning the gas rod area, gas tubes, or gas inlet.
Wipe the gun clean with lint-free cloth (you can buy pre-cut cloth, but a clean old shirt or socks also work). Get everywhere you put the solvent (should be pretty much everywhere) and wipe it until it wipes clean.
Wipe down the whole gun (inside and out) with a solvent-soaked lint-free cloth again, and look again for any areas turning the cloth dark, and clean it.
Use the pick to get off any thick chunks of carbon or powder buildup, or buildup in tight parts of the gun.
The most common area with carbon deposits is in the chamber. Buildup occurs in the corners of the pieces of metal.
Clean the Barrel
Use a bore brush to break any buildup free from the barrel.
Run the full length of the barrel at least five times (more if you have shot a lot since the last cleaning).
Be sure not to reverse direction with the brush (in the barrel), push it all the way through, then all the way back (letting the bristles changed direction outside of the barrel).
Swab the barrel with a cloth soaked with solvent. Repeat with clean cloths (still soaked in solvent) until a cloth comes out clean. Run the swabs from the receiver to the muzzle (in only this direction).
The number of times needed to clean the bore will vary greatly depending on many variables. It may take as many as 20+ passes to clean the barrel properly on a very dirty rifle.
Use a bore guide to prevent rubbing the metal rod against the initial rifling.
Use a rod which is made from a soft metal like aluminum. Harder metals can easy scratch your barrel.
Swab the barrel with a cloth soaked in copper solvent. This removes any copper which may have come off of a jacketed bullet during it’s travel down the barrel. A few passes may be required (repeat until no copper particles are visible on the cloth, then do it once more).
Do not oil your bore. There is no advantage to adding gun oil down the barrel, and this increases the chance of buildup of dust and powder/copper/lead residue which can lead to jams and squibs (when a bullet gets caught in the barrel). Contrary to popular belief, oil does not neutralize solvent.
Swab the barrel with a dry cloth before you start shooting. This produces consistent results and ensures the solvents are neutral, while keeping your barrel dry for the first shot.
Clean your barrel every ten shots if you require top accuracy. The bore brush is not a required step for standard cleaning, but may be desired for a complete clean.
Finishing Up
Oil all the components requiring lubrication. Often the manual for the gun will have specific areas needing oil, but a quick look at where the gun is wearing will give you a good indication of the needs.
Be sure to oil the areas around rotating parts, such as the bolt and trigger assembly.
Try to keep oil away from the openings into the firing pin housing (oil is a collector of dirt and powder buildup, and buildup around your firing pin can prevent it from firing).
Don’t forget to oil the bolt rails and the grooves in which they ride.
Reassemble the rifle and make sure all parts are functioning properly.
Wipe down the whole gun and remove any excess oil.
Tips
If you are having a tough time with some thick buildup, apply more solvent and let it soak for a while.
If you aren’t able to get all the areas solvent has gotten into, no worries. The solvent will eventually evaporate or the oil you spray on later will neutralize it.
A very light (almost invisible) coat of oil on the exterior of metal parts will prevent rusting by preventing moisture saturation.
This pretty much describes the cleaning, we were required to do on our M16’s in the military. Quite honestly, some “War Games”… I didn’t even shoot a round off…. that would cut cleaning time in half… 
One hint, when it is a rainey season like the last, I carry Rem Oil clothes with me, to wipe down after a wet day in the field…. once a rust spot starts, it doesn’t magically go away… you have to stay on em 
Good reminder post Ruger 
Between the bore snakes and Rem Oil patches, taking care of our guns everytime we’re in the field really eases up on the annual chore.
