Pellet Gun Cleaning Patches From Used Dryer Sheets

Commercial cleaning patches are made from  a non-woven material, are approximately 1-3/8 in. square and cost about $2.50 USD per 100.  Unless you are very anal retentaive and clean them after use using a de-greaser dish detergent, rinse well and let them dry - the rest of the world tosses them.  There is a less expensive alternative.

Save up a few used (see image, NOT the plastic sponge type) dryer sheets.  I usually stack four at a time, cutting them into six columns along the long side.  Then these I cut into four pieces.  Each dryer sheet yields 24 patches. 

Simply fold each patch into a triangle, insert the folded edge into the cleaning loop, as with a stqandard cleaning patch.

Airgun barrels do get dirty. They collect dirt in the bore from the oil in the barrel. Oil gets there for many reasons.
In spring guns, the mechanism puts it there (through the transfer port). In pneumatics and gas guns, we sometimes oil the pellets.  Some pellets even come pre-oiled or waxed. So barrels do get dirty, but the deposits don't remain inside.
Do not use cleaning fluids meant for regular firearms, they will ruin the seals in your air gun.

Every pellet down the barrel scrapes out the deposits from the pellets that went before. This is why many airgunners never clean their barrels.

Faster velocities and hard pellets can deposit lead in the bore.
As velocities climb above 900 f.p.s., some pellets will leave streaks of lead on the surface of the bore.
Hard pellets are the worst. Pure lead pellets are soft and don't leave lead deposits as easily, but pellets that have antimony in their alloy are harder and more prone to scrape off. Try to scratch the head of a pellet with your fingernail. If it's soft, you'll be able to leave a sratch mark - but you won't leave a mark it if it's hard.

4 rules for the proper cleaning of airguns -
Unless you know your barrel has lead in it, all you need to do is:

1. Run several clean patches through the bore to remove the dirt and grease. Remember, you DO NOT have to do this unless you want to!  any Olympic champions do not clean their airguns - ever! But there is no harm in cleaning, unless you make some fundamental mistakes.

2. Clean from the breech if at all possible. You want to protect the rifling at the muzzle because damage there will spoil the gun's accuracy.

3. Do not use solvents to clean an airgun. A good grade of gun oil on a patch will remove the dirt, but keep that to a minimum.

4. Dry the bore after cleaning unless the gun is going into long-term storage, in which case a light film of good gun oil is best.

Dispose of the patch properly after its use.  You might need to run a few patches in sequence per cleaning.