Methods of barrel break in and care varying greatly, so I'll just share what I do and why. Yeah, I actually gave this some thought at one time.
Anyway, I don't think that many will disagree that over cleaning is a bad thing. I've read many article that tell us that cleaning does more to wear the barrel than normal use does. Following this line of logic, I don't give my barrel a good cleaning until it starts to show a degradation in accuracy. The key for me is to have a barrel that can shoot lots of rounds before it needs to be cleaned and this is where I believe a break in procedure is important.
The purpose of breaking a barrel in is to smooth out the machine marks in the barrel, most importantly the marks at the throat. To smooth out the throat/bore, you have to shoot the rifle, but every time you shoot the rifle, copper fouling builds up at the rough areas keeping the parts that you need to smooth out from getting smoothed out. So, you have to remove the copper fouling to allow the smoothing out process to proceed as it should.
I do not, however, believe in any strict procedure, like shoot once and clean for five rounds, the shoot five and clean for 15 rounds, etc. I believe that a barrel will tell you what it needs and how much breaking in your barrel will need varies.
I usually do an initial cleaning. I shoot one round, run a patch wetted with Butch's, then use another wet patch to scrub the barrel paying attention to the throat area. I then run a dry patch and take note of the amount of blue that I have on the patch. For the very first round, you should have a good bit of blue on the patch. I do this until the amount of copper (blue) that I get is significantly reduced, then I go to cleaning once every five rounds, until I get no blue on the patch.
How much cleaning you have to do depends on how rough the bore/throat are. I have to admit that I now have only one rifle that has a stock barrel on it. My other rifles have Kriegers on them and I've never had to shoot more than ten rounds before I felt that the barrel was broken in.
