in response to those advocating the use of a live center and a crown insert/protector- I have never used this method, and will not say that it is an improper method to use, but I do think it is not the best method to use. IMHO, the best method is to use a lathe that has a short enough headstock and large enough spindle hole that you can pass the barrel through the headstock and indicate the center of the bore of the barrel on both ends. This will require that you make a "spider for" the spindle of your lathe. This is nothing more than a collar with four adjustment screws that is mounted on the end of the spindle (opposite the chuck). Use a four jaw chuck and indicate in the bore, with only a few inches of barrel protruding from the chuck. This insures that the bore of the barrel is now concentric to the machine.
Using a live center will only insure that the bore is centered at the point that it meets the live center. This is not the same as being concentric, because you are still relying on the outside diameter of the barrel on the end held in the chuck. Indicating on the OD of the barrel does not guarantee that you will be working concentric to the bore. I have seen barrels that were not concentric (OD to Bore) by as much as .015".
The crown protectors may work, and you may never have a problem with this method, but it really is not the "best" way as you are still relying the the OD of the barrel to be concentric to the bore. If your lathe headstock is not short enough, or the spindle hole is not large enough to pass a barrel through, a better alternative, IMHO, is to use a center mounted, and indicated to perfection in a four jaw chuck, and then drive the barrel with a lathe dog. The downside to this method is that you are now relying on the breech face of the barrel to be cut square to the bore. Once again, I have found this to rarely be the case, but having tested many barrels over the years for concentricity, I have found that this method is superior to using the OD of the barrel in a three or four jaw chuck.
While any of the methods talked about will probably work for most applications, rifle accuracy is affected by a host of variables. Getting the crown perpendicular to the bore can make a big difference by causing the gasses behind the bullet to exit the muzzle evenly, rather than offset by whatever amount the crown is not square to the bore. This can slightly upset the bullet as it leaves the barrel. The ONLY way to get the crown square to the bore, for certain, is to indicate both ends of the bore. This holds true for threading a barrel too. It may or may not make a difference, but using this method, I KNOW that I have done everything that I can do to make the crown, threads and breach face cuts as perfect as I can. This cannot be said of any other method, as you will be relying on the OD of the barrel being concentric to the bore with any other method.