Wet a patch with a good bore solvent ie. Hoppe's #9 or similar, push it through the bore from the breech to muzzle allow the solvent a few minutes to work then put several dry patches through until you get little or no "crud" on your patch. I usually use another patch with Hoppes on it if I'm storing the gun oil will be good for storage too. Before shooting, put a dry patch or two through the bore to remove the oil/cleaner will give you better first round accuracy.
Do not shoot rapid fire or a large volume of ammo without cleaning your barrel like this for the first 100 rounds. After a large volume of rounds (100+) more serious cleaning methods are recommended. This is where a bronze bore brush comes into use.
There are several schools of thought about the usage of a bore brush, one says a dry brush followed by solvent on a patch, another says a wet brush followed by dry patches. If your bore solvent has copper removing chemicals DO NOT WET YOUR BRONZE BRUSH. Bronze is an alloy of copper. A non copper removing solvent is OK to wet the brush with. There is no danger from the use of a bronze or nylon bore brush stainless steel should be used only for very difficult deposits and with extreme care.
A one piece coated cleaning rod is a great investment, as is a bore guide. I love a Boresnake, but it does not take the place of a proper cleaning with a rod, brush and patches.
For AR 15 rifles a chamber brush is a necessary cleaning too. A dirty chamber and dirty locking lug recessed account for more malfunctions with AR pattern rifles than anything else.
Enjoy your new rifle.
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