Here's what I've done specifically for the barrel of every gun I've gotten.
Run a couple dry patches through the barrel. This gives you a quick determination of any obvious burs and general level of cleanliness.
Run a couple of wet patches through the barrel. This gives you a quick determination of any tight spots and cleans the barrel regardless of the level of cleanliness. Then a couple dry patches.
Go to to the range to sight in and put around 100 rounds through it. This will give you a nice fresh lawyer of fouling and either work out any trouble spots not detected earlier or alert you to trouble.
Come home after the range trip and run a couple of wet patches followed by a couple of dry patches until the patches come out clean.
Put it away knowing it's good to go.
EDIT: To reiterate, this is just what I do, everyone has their own rhyme and reason and therefore it is just to show you exactly that.
Also, I use quality ammo for this process.
Last edited by Revoliver; March 9, 2013 at 02:00 AM.