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.