Cleaning is one of the most important parts of gun care and respect. The more you respect them, the better. I'm not going to give you a speech :).
Also, especially with a military relic like this, taking care of the rifle keeps its value high and makes it perform a heck of a lot better.
-Cleaning Rod, at least as long as the barrel of the rifle you are cleaning. Check Wal-Mart.
-Cleaning Patches, for the caliber rifle you are using. Can be found at most sporting goods/ gun s tores, even Wal-Mart
-Solvent, whether it's Hoppes 9 or Gun Scrubber it doesn't matter. This can be found once again at sporting/gun stores and most of the time Wal-Mart.
-Rust Protector, like Barricade in the photo or others.
-Some way to hold the rifle in place, I used sandbags made for shooting and a regular vise with a towel draped over it keep it from marring the wooden stock. They do make gun vises just for this purpose and if you are doing a lot of cleaning, you should consider getting one. Last I checked they ran from about $50-$200.
-Disassembly Tools, you need the tools that are required to disassemble your rifle. Often this is none at all or just screwdrivers. Some rifles have special tools (ie. M1 Garand, Mosin Nagant, SKS/AK sights) that are made just for them. Most of the time they are not necessary and can be replaced by normal consumer tools, but help a lot.
-Disassembly Guide, how are you going to clean it if you cannot take it apart? Some rifles come with a manual from the company that imports them (mine was from Century Arms) and you can buy take-down guides at most gun stores. Also, you can find instructions on how to take-down military rifles at SurplusRifle.com.
-Place to store small parts, not really required but helps a lot. I found a small organizer in the sewing (I think?) department of Wal-Mart. I can't tell you how many times I have dropped a screw or something of the like and spent hours searching for it on my garage floor. It's nice to have them all in one place.
-Last but not least, a spacious place to work, I use the workbench in my garage, but most places will do. You need at least enough room to fit the cleaning rod down the barrel. Remember that most of the solvents and chemicals need to be used in a well ventilated area, so do so. Personally, my garage workbench is a little too small, but it will do.
WARNING: Guns by nature are dangerous, and I hope you would know that. Always make sure the gun is not loaded in any way. In addition, some of the chemicals or solvents used when cleaning are toxic to breath or touch. Where the proper safety equipment (gloves, respirator, etc.) And for God's sake don't get the stuff in your eyes, or you will be sorry (I know from experience!) Therefore, while cleaning a gun shouldn't be dangerous if you do it right, I am not liable for any injury or death sustained while doing this. Don't be stupid or careless, always use proper gun safety even when its not loaded, and while cleaning. PLEASE BE CAREFUL.
Step 1: Make Sure the Rifle Is UNLOADED!
You wouldn't want to be killed (or kill someone else) by the unloaded gun would you? This takes all of 20 seconds but is a crucial safety step.
Well, you get the point, don't be stupid and careless!
Step 2: Partially Disassemble the Rifle.
For the Mosin-Nagant taking out the bolt is simple. Just pull the bull to the rear, pull and hold back the trigger, and pull the bolt rearward out of the receiver. To take of the PU scope, I just unscrewed the bolt on the base and removed the mount and scope.
Step 3: Visual Check and Wipe-down
Next, I think it helps just to wipe-down the rifle with a paper-towel or the like. A lot of the dust and dirt on the stock (from the range) will come off and any grease applied last cleaning (to lubricate) probably has grime stuck in it to. Wipe it all off.
Also, while not necessary for this one, I would advise putting a towel over the wooden stock in areas that you might spill the solvent. That stuff will eat through the finish and can ruin the stock.
Step 4: Barrel Cleaning
Insert the rod at the muzzle and push it towards the butt of the gun.
When the rod comes out of the barrel and into the receiver, DO NOT pull it back through the barrel. Take the patch off and then pull the rod back out the way it came. Pulling the rod out with the dirty patch in it could get the dirt you just cleaned back in the barrel. I don't really know if this is true, but it is what most people tell me and it seems logical.
Continue to put solvent on and run them down the barrel until you get the bulk of the mess and break up the solids in there. You can check your barrel buy looking down it (duh).
After a while, you can just run dry patches until they come out white. It might take quite a few of them, so don't stop mid-way.
NOTE: If you have a copper brush, use it now too. They help a lot. I just don't have one for this rifle so I didn't use one.
Step 5: Clean Other Metal Parts
Be sure and check to make sure that the solvent will not take off the finish on the metal. Things that are painted (some civilian sporting rifles) may be affected by the powerful solvent.
Step 6: Stock Treatment
Step 7: Rust Protection
Spray it onto a paper towel and wipe it on other parts like the outside of the barrel, sights, receiver, etc.
In my opinion this also makes the metal shine a little bit too.
Step 8: Lubrication
Just be careful when using a Cue-Tip not to get the little fuzzy parts on the ends in the lube and then in turn in the rifle.
Step 9: Reassembly and Glamour!
It helps to do that every time you fire about 50 or more rounds out of it. Now I know that a military rifle like this doesn't need it that often, but I hate to put it away dirty. Plus, doing it often makes it not as large of a job.
This may not be perfect, and feel free to post up your methods (comments, other instructables) and suggestions.
Happy shooting, and thanks for reading.