H3At you got a good cleaning rod. You need to got to Georgia Precision (look in the Industry section of this site) and get yourself a bore guide. This slips into and is somewhat locked into the chamber by way of an o-ring. This keeps the rod centered in the bore during cleaning so as to not damage the bore or the crown. Get the one with the solvent port in it. I cuts down on the mess created by running a soaked patch into the back of the guide. I would suggest you get a chamber cleaning rod from them as well. The handle on these don't spin freely. If you get one you'll see why the first time you use it.
The rod rotates so the patch or brush can follow the rifleing in the barrel. Put the jag on the rod, push a patch onto the point, insert into bore guide to the solvent port, apply cleaning solution of choice, and commence to cleaning. You can reverse the direction of a patch on these jags as they give a nice snug fit. I never reverse the direction of bronze brushes in the bore. I will however scrub in both directions with a nylon brush, which I would recommend you to use anyway. If you use a copper solvent be sure to use the nylon brush as the solvent will attack the copper in the bronze brushes.
Enjoy your new rifle man. Keep her clean and ready and she won't let ya down when you need her the most.
Shabo