The search function will reveal several threads on this.
As a minimum, it would seem that it is a good idea (for a match barrel) to shoot a single round, and then clean with a copper solvent, and repeat that procedure for every round for at least five to ten times. Then, shoot three rounds, stop and clean and repeat at least five times or so, and then perhaps move on to bigger "batches" of rounds between cleaning.
As I understand it, the purpose is to get the copper fouling out of the barrel while it is still "polishing" itself (getting manufacturing irregularities out) during the first 20-50 rounds.
Depending on the barrel, some will get broken in faster than others, but the consensus seems to be that some kind of procedure like this is important for stainless match barrels.
I'm just getting my first couple of stainless match barrels myself, so I am interested in understanding this too (and want to see what the other responses might be).