Another recommendation for Patch Worm. And be careful of any cleaning solvent you use as not all are friendly with rubber o-rings, like the breech seal. Ballistol, as recommended above, is good.
I turn the gun upside down so no fluid gets into the transfer port, pull with the Patch-worm a couple wet patches. Then dry patches till clean. Fire a couple times upside down to make sure no fluid in gun. I hate to remove barrels to clean. OH Balistal.
Ballistol and patch for me as well however you can use a string with a loop at the end and just use patches or t-shirt scraps too. I love the patchworm tho.