Cleaning Procedure
I'll start by a dry patch down the barrel, and a dry patch in the chamber to get all the oil out I applied after the last cleaning.
Then I'll shoot the rifle.
Then...
I use a carbon/powder residue solvent and a bronze brush first, (run all brushes and patches from chamber to muzzle.) I run about 10 swipes, then run a dry patch.
Then I apply a copper solvent with a nylon brush, I'll apply a newly solvent soaked brush 5 times on my 22 inch barrel. I'll let that sit for 5 minutes then run a dry patch through.
I'll examine the patch and muzzle, if the patch is dark blue and bore shows more signs of copper, I'll repeat the copper cleaning until the patch comes out light blue and/or I see no copper in the bore.
Then I'll repeat the cleaning procedure for carbon/powder residue until the patch comes out clean. I also use a chamber brush to get any carbon or what have i in the chamber during this phase.
I'll run a bronze brush of oil then dry patch, then an oil soaked patch. I'll run a oil filled cloth in the chamber... making sure the barrel and chamber are not going to rust.
I usually take one or two shots a day, cleaning my bore for carbon/powder residue only; after 10 shots I'll then clean for copper also.
Break-in Procedure
Here is what I did when I broke-in my new Howa during load development, (had 20 ladder test cartridges.)
I cleaned the bore thoroughly as above.
Shot one shot.
Cleaned as above, (most of my focus was on making sure there was no copper.)
Adjusted my scope, (I was bore sighting too.)
Took another shot.
Cleaned as above, (most of my focus was on making sure there was no copper.)
I repeated that procedure; (shot then cleaned,) for 20 shots, (as to not skew my ladder test.)
If I was just shooting factory ammo and simply sighting the scope, I would have shot 1-5 cleaning after each shot. Shooting shots 6-11 cleaning every other shot. Then finishing with shots 12-20 cleaning every third shot.
...
I just wanted to point out that you can still do other things during the break-in period. I came away with a zeroed scope, a few charge weights to test, and a bore that copper fouled a lot less than it had been.