I remove the bolt and then take the center of the bolt and the main housing apart. After that, I remove the breech plug. The first thing I do is clean the breech plug. I then take an alcohol patch and wipe off the firing pin the coils of the bolt, and using Q-tips clean the face of the bolt off. After that I wipe the inside of the bolt housing out.
Now with that area clean, I wipe out everything I can reach. I then saturate a patch and push that into/over the breech threads. I then work that back and fourth scrubbing the threads. And then push that out through the muzzle. Again, saturate a patch and scrub the threads.. push that out the muzzle. When I have the threads looking clean, I start to push dry patches over the threads, and then up through the barrel. Once every thing is nice and clean, I wrap the breech plug up and replace it. I oil the bolt and put that back together. I then oil the bore of the barrel and wipe off the outside.