If you don't have a cleaning kit, get one. It'll contain a brush and a slotted "thingy" thatscrew on the end ofthe rod. You can thread a bit of patch through the slotted "thingy", (enough to get a tight fit), or wrap a patch around the cleaning brush. Clean from the breach end of any rifle. If you bang up the rifling at the muzzle witha cleaning rod, you'll ruin your accuracy.
My "usual" procedure is to dip my brush in a copper solvent, (Butch's Bore Shine, Hoppe's Bench Rest, etc.) I give the bore a good scrubbing, followed by dry patches to clean out the residue. I then use a patch with a small amount of oil or WD40, and follow it with more dry patches.