Basic bolt action rifle cleaning and maintenance
Its important to clean your hunting rifle every quarter if you havent used it, and after each trip to the field or range. The primarily area of attacking the burnt carbon, metal shavings, and corrosive primer chemicals left behind by every range or field session is the barreled action. With a safe and unloaded weapon, with no brass or ammo around, remove your bolt and set it to the side.
Next, use your cleaning rod in the same direction that the bullet travels-- breech to muzzle-- to clean. Begin with a good commercial solvent made specifically for firearms such as Hoppes No. 9 or a multipurpose cleaner-lube-protectant such as CLP or Ballistol on a patch that is the right caliber for your barrel and work it through then let it soak for a minute or so to help get into that gunk.
Then run a cleaning jag down your barrel, remember from the chamber side to the muzzle, to break it up. Follow this up with a clean patches on your rod until they come out as white as they went in.
Then address your bolt. Remember that bolt-action rifles all typically harken back to the old days of the Mauser, Enfield, and Mannlicher guns that were designed and made for barely trained foot soldiers to care and maintain these animals in the field under harsh conditions. As such, these bolts actually need little cleaning. Typically you can wipe down the locking lugs and bolt bolt face with a solvent impregnated cloth or rag, hit it with a brush, wipe it clean, then apply just a very thin coat of lubricant.
When I say thin, if you put more than what you can fit on your fingertip in your rifle action that is far too much. Keep in mind that over lubrication can be your worst nightmare in the field as that product will reach out and grab every fleck of dandruff or particle of rock and sand then drag it deep into parts of your action that you have never even imagined.
On the barrel, run a lightly coated patch with your lube or multipurpose clp on it, again from chamber to muzzle, to get a light sheen in your rifling. Some advocate leaving a wet patch impregnated with your lubricant in the barrel, which is a good idea for long-term storage, but if you are a regular shooter that takes the rifle out to the field or range often, its likely overkill. Also, remember this patch and check your barrel for possible obstructions before you go hot.
Modern Sporting rifles
For cleaning an AR-style semi auto, make sure your gun is safe first. Then, point the muzzle in a designated safe direction and place the selector lever on safe. (Hint: if weapon is not cocked, the lever cannot be placed on safe.) Next, remove the magazine by depressing the magazine catch button and pulling the magazine down. Then lock the bolt open and pull the charging handle rearward. Press bottom of bolt catch and allow bolt to move forward until it engages the bolt catch. Return charging handle to full forward position. Then inspect the receiver and chamber to ensure these areas contain no ammo. With the selector lever pointing toward safe, allow the bolt to go forward by pressing the upper portion of the bolt catch. Place the selector lever on semi and squeeze the trigger. Pull the charging handle fully rearward and release it, allowing the bolt to return to the full forward position. Place the selector lever on safe.
Next, field strip it into the upper receiver, bolt carrier group, and lower receiver group. On the upper, using a light coat of a clp product or solvent clean all areas of the bore, locking lugs and gas tube (if direct impingement) then lightly lube them. On your bolt carrier group, be sure to pay attention to those inner surfaces, carrier key, ejector and locking lugs. On the lower, you can just wipe it down but be sure to check that buffer spring and the tube.
Finally, in all types of rifles, storing your firearm again, give it the once over/all over wipe down with a clean rag to include the muzzle crown and consider storing it in a climate controlled cabinet or safe with proper desiccant-- especially if you live in a humid area and have a wooden stocked rifle.