You will hear plenty or versions. Others might even say it is a waste of time and money. "I" have a slightly modified version of Lilja's break-in procedure ...
For an effective break-in the barrel should be cleaned after every shot for the first 10-12 rounds or until copper fouling stops. Our procedure is to push a cotton patch that is wet with solvent through the barrel. This will remove much of the powder fouling and wet the inside of the barrel with solvent. Next, wet a bronze brush (not a nylon brush) with solvent and stroke the barrel 5-10 times. Follow this by another wet patch and then one dry patch. Now soak the barrel with a strong copper removing solvent until all of the blue mess is removed from the barrel. The copper fouling will be heavy for a few rounds and then taper off quickly in just one or two shots. Once it has stopped or diminished significantly it is time to start shooting 5 shot groups, cleaning after each one. After 25-30 rounds clean at a normal interval of 10-25 rounds. Your barrel is now broken-in.