I clean my Trap guns after every outing. I have compressed air, so I start my washing out the barrel breech block and receiver of my Citori O/U and BT-99 with clean Kerosene, (available in one gallon jugs at Tractor Supply), and a stiff bristled paint brush. I do the same with the receiver of my pumps and semi autos.
I just be sure to hold the butt stock higher, so all the Kerosene drains away from the stock, and out the end of the receiver.
This washes all the dirt and old lubricant out, and after a good blowing with compressed air. They are 100% clean and dry. Then I take a Super Unscented Tampon, soak it with Hoppes #9, and push it down the bore with a cleaning rod.
Tampons work the best for this because they're larger and more absorbent than those 12 ga. cleaning patches, that I've found to be all but worthless. Just be sure to buy unscented tampons. You don't want a shotgun that smells like, "Summer Rain".
After the Hoppes #9 soaked tampon, I follow with a bronze brush. (I don't like Stainless Steel "Tornado" type brushes because they can scratch the bore). Then another Hoppes #9 soaked Tampon, followed by a dry Tampon. After that, I run an oil soaked Tampon down the bore several times to give the inside surface a nice, light coating of oil. They fit just as nice as those "Mops" that screw on to the end of your cleaning rod, but they're far cheaper, and they are disposable.
On my BT-99 and O/U's I'll lightly grease the hinge pins, contact points, and trunnions. Reassemble everything, and I'm good to go. With my semi auto and pump shotguns I use oil instead of grease. But otherwise they get the same wash and blow dry treatment. It's unbelievable what will wash out of these guns with the Kerosene treatment. (If the smell of Kerosene bothers you, you can use WD-40). It comes in gallon jugs as well. You are going to blow everything dry with the compressed air, so the WD-40 won't gum up. It has a sweeter, better smell housewives are less likely to b!tch and moan about.
I usually remove screw in chokes after every 400 targets or so. Give them a Kerosene wash and blow dry. Then coat the threads with Loctite C5-A copper anti seize, run them in and out a few times to disperse the anti seize throughout the threads, snug them down, and that's it.