Slipery, you recieved some good replies from other members but here are just a few details to add on.
This is my post from the 10/22 tips section on cleaning
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I use a Dewey .20 caliber coated rod for cleaning my .22’s. There are obviously much better rods out there but for me this rod seems to work well. Other choices include pro-shot, kleen bore, ect.
For solvent I use Butches bore shine. I find this solvent works better for me then hoppes number 9, and so far all others I have tried. Some choose to mix this 50/50 with the penetrating and lubricating oil “Kroil”. I have never tried this my self but I have heard many good reports about using this stuff from top-notch benchrest shooters.
Rimfire Cleaning
In the past years, endless debates have arose regarding the proper cleaning of both rimfire and centerfire firearms. There are many opinions on how to clean any given firearm. Some say cleaning with a brass brush is a necessity, when others people argue that cleaning with a patch and a bit of solvent will do the job without any risk of damage.
I strongly believe in the use of a brush every once and a while to get rid of the lead that builds up in the bore, and the chamber area especially overtime. Not necessary every single time but maybe every 500-1000 rounds a pass with a brass brush won’t do much damage. I use a nylon brush quite frequently in many of my benchrest rifles along with y 10/22.
There are many things that need to be paid attention to when cleaning. You need to make sure that you are using the correct size brush and rod, you have to insure the equipment you are using is good, and many other things.
The first step to insure proper cleaning of a firearm, is to insert the bore-guide. Make sure that the bore guide fits into the gun properly so that the cleaning rod slides into the chamber without hitting any edges, and so that no access cleaning solution can enter or damage the trigger mechanism.
In the case of cleaning the 10/22, you can not insert a bore guide without drilling a hole in the back of the receiver or removing the barrel all completely. In this case you must be very careful when inserting the cleaning rod through the muzzle (that is if you didn’t or don’t have a hole drilled in the back of the receiver. A simple muzzle guide that can be purchased for about $3 can help reduce the chances of hitting the crown when cleaning.
Before putting the cleaning rod into the gun, make sure that no grit is on the cleaning rod (if so, wipe off with wet paper towel and dry and with a dry piece). This will insure that no “grit” can damage the barrel of the gun.
What I first do when cleaning is I run a quick wet patch through the gun. This is a patch that has cleaning solvent on it. Just one pass is fine. This will remove the majority of the “gunk” out of the barrel.
After I have run a wet patch through it, I usually use a nylon brush to remove all of the lead and carbon that could possibly built up in the barrel. One nice thing about the nylon brushes is that you can reverse it in the barrel. That is, if you pushed it half way through and then wanted to pull it back you could do this without too much difficulty. With the brass brushes it is very hard to do this without a lot of force. It may even be possible to damage the barrel this way. You can also pull it back and forth through the muzzle without damaging anything if you are careful. Now with the nylon brush attached to the cleaning rod, I run it through the barrel about 5 times (1 time = back and forth). I also dip it in the cleaning solvent before running it through (but just the one time, not each pass)
Now that the gunk is “knocked out” from the rifling and the bore, you have to remove it from the barrel. To do this I simply run 2 dry patches through the barrel to remove the gunk and any leftover cleaning solvent.
After this is all done just wipe off the crown to remove and gunk and the gun powder on the outside.
Now you are all done. I also usually wipe down the gun with a silicone cloth. This may sound like a long procedure but it really doesn’t take that long.
On my bolt action guns (not on my 10/22) I push a brass brush through it 2 or 3 times removing it at the muzzle each time. I do this every 500-1000 rounds.
Each gun has different preferences for when to be cleaned. I clean usually every 50-100 rounds on my benchrest guns when using target ammunition. When using the bulk type gun out of other guns I clean every 200 rounds or so.
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This was written about a year ago but my procedure has basically stayed the same as i have found this to work well for me.
One comment I would add is DON'T use the 3piece alluminum rods that you buy at Walmart, etc. They are no good and will do more harm than good to your barrel. Get a good 1 piece steel rod.
Hope this helps

Jordan