swifty,
No secrets to chamber polishing.
First make sure that you need it! Does the chamber have visible reamer marks (rings)? Do you have annular rings on your fired brass? Are fired cases difficult to extract? If the answer to most or all of these is YES, then a little chamber polishing will only improve your rifle.
Use a 3/8" or 1/2" plastic or wooden dowel to back up the polishing media. Saw a slot lengthwise on the dowel. Wrap very fine wet-or-dry sandpaper (600 grit) in strips long enough to cover the entire chamber while you work. It's safest to do this by hand, but after gaining a feel, you can CAREFULLY use a slow drill motor, lathe, or drill press for this. Carefull in-and-out motions combined with rotating motions does the trick.
The object is to only POLISH, and not to enlarge the chamber. Only a couple minutes of this is needed. Work slowly, until the bulk of the chambering tool marks are gone. Be carefull not to enlarge the front of the chamber or the bullet seat area. Follow up by this using crocus cloth, and you will have a chamber that shines!
Test firing should produce easier extraction, and no chamber marks on your brass.