Trout,
The traditional technology for this is a bit different from some of the modern technology sometimes used in making modern production barrels. So if you just search reaming or rifling on this site, you may be left with some confusion about what they are describing.
The traditional reamer for polishing the bore is long cutter, a few inches in length, that is usually square in cross section and slightly tapered. It is pushed or pulled through the bore and is rotated as it passes through. The cutting edge is along the length of the reamer, and it scrapes the bore as it rotates—that is to say it cuts on a rotating stroke.
In contrast, traditional rifling cutter is pulled. It does not cut on a rotating stroke, but rather on a pull stroke. Thus is it shaped like a very short, thick hacksaw blade, and the groove of the rifling is literally a saw kerf. If it were to be pulled straight through, then straight rifling would result. (A similar effect would result if you just passed a hacksaw blade through the barrel and sawed a straight groove into the inside of the barrel tube.)
If you put that short, thick hacksaw blade on the end of a long shaft and attach the shaft to a slowly spiraling machine, that machine will cause the cutter to spiral slowly as it is pulled through the bore. The result is a kerf that spirals, rather than being straight. To get seven such evenly spaced kerfs cut into the bore, the spiraling machine has seven corresponding positions into which it will lock. Each position corresponds to a different groove in the final product.
To move the cutter from one groove to another, the machine is just moved from one of its lock positions to another. The rifling machine is usually made of wood. The positions are defined by seven wooden teeth in a box that correspond to seven notches (grooves) in a long wooden spindle. To move from one position to another, the spindle is withdrawn from the box, rotated slightly, then repositioned in the box.
The cutter only cuts one groove at a time, and the same cutter is used for each groove. The height of the cutter is gradually adjusted by putting paper shims underneath it, so as to lift it up a few thousands of an inch at a time. So each groove is cut once at a particular height. The cutter is then raised the thickness of one shim, and then each groove is cut again at the new height. The eventual result is seven equally spaced grooves of equal depth.
The following links show images of these tools and processes.
Traditional, square barrel reamer:
http://americanlongrifles.org/forum/index.php?topic=30175.0Traditional, hacksaw-like rifling cutter (and corresponding wooden rifling machine):
http://americanlongrifles.org/forum/index.php?topic=30643.0