Set up rifle in a cleaning vice, like a Tipton.
spear a patch on a proper fit jag on a 1 piece rod
soak patch in your solvent of choice (I like Warthog bore cleaner): http://warthog1134.com/
push rod/patch through bore guide and soak bore a couple of strokes. Repeat with 2 new soaked patches.
Push one dry patch
push bore brush (wet with more solvent) through bore about 10-20 times. If you are really anal about the crown, unscrew the brush prior to drawing it back through the muzzle and reattach before each pass. I drag it over the crown very slowly myself.
push 2 dry patches, then another soaked one, then another dry one and check color of patch for fouling. If cleaned to your satisfaction, push a patch with oil on it through the bore prior to storage.
I also like KG supplies. I like their carbon solvent and copper solvent. follow their directions.
OR, Finally, get some wipeout or gunslick foam and fill the bore. Let it sit for as long as you want, even til the next day. Push dry patches through. Keep in mind, the longer a foam sits in the bore, it will lose the foam consistency and turn to liquid, settling on the downside of the bore due to gravity. I did some foam cleaning on a rifle with wipeout 2 days in a row, laying the rifle on each side and upright in a Tipton vice. That worked pretty well. No brushing needed on that occasion.