Not much too it really. Just use whatever cleaner turns your crank among the various choices of Hoppes, Shooter's Choice, etc. I tend to buy whatever is cheaper or available at the time.
First off, if your cleaning rod is anything other than a one piece, you need a new cleaning rod that is--you guessed it--a one piece rod. Remember to wipe the cleaning rod down between strokes.
Next you need a bore guide. It'll go a long way to keeping your cleaning rod moving straight through the bore, in addition to keeping cleaning solvents from dripping down into the action.
Pickup one of the military cleaning brushes. It's the toothbrush that has bristles at both ends. That'll take care of most of the scrubbing chores. For very stubborn carbon deposits, a bronze bore brush works very well, if not difficult to manipulate in comparison.
Pickup some of those microfiber towels (many automotive store sell them) for where you need towels. Avoid paper towels as they leave lint and pieces scattered around. Make sure you wash them so they don't get loaded down with debris that can scratch the surfaces of your guns.
A cleaning mat is a good idea. It keeps your work surface clean and will help protect your marriage when you drop a bolt onto the tile of the kitchen counter.
Now that you are armed with the proper tools, just get to work cleaning what you need. I like to pour a little solvent into the container's cap to use for dipping my brush in. Custard bowls procurred from the kitchen also have many uses on the cleaning and loading bench, much to my wife's chagrin.
Pay attention to the bolt face and the extractor and ejector. Make sure there isn't junk there will prevent their proper operation.
Be careful with which oils you use in the firing pin channel. You need something to protect against corrosion, but that won't thicken up in the cold and slowing down the firing pin causing misfires. I like FP-10 for oil. Rem oil is pretty good. Militech seemed to thicken more than I cared for in the cold. Some folks like Mobil-1. Whatever you use you don't need to lube it up like a automotive chassis. A little goes a long way. Use whatever you like. If you want to be hardcore and test your oil of choice out, load a piece of brass with a primer only and put your bolt in the freezer for a few hours then see if it'll still pop the primer.