Rather than write some war-n-peace length post on barrel cleaning, I figured it might be better to just give you some links to some reading material. Short version is that for most bolt guns such a Savage you can pull the bolt, stick in a bore guide, put a 'boot' or other protective cover over the cheekpiece of the butt stock and clean from the breech, and on guns like an AR, you'd pop the rear take-down pin, pull the charging handle and BCG, insert the bore guide thru the upper receiver into the chamber and again clean from the breech end. On a 10/22 I'd either pull the barrel (drop the stock and then loosen the two bolts) or clean from the breech with a bore snake. Guns like an M1/M1A or most lever actions you don't have much choice other than to use a snake or clean from the muzzle.

http://www.accurateshooter.com/techn...and-materials/
http://www.accurateshooter.com/techn...eaning-debate/
http://www.accurateshooter.com/gear-...m-bore-guides/