Setup (60 to 75% of time), Thread for action, Short chamber, check fitment to action, Concentric ( parallel ) to bore? (not in that exact order, some check barrel to action fitment). Now this part some smith remove the barrel from the lathe for checking fitment to action, most the one I know don't because if incorrect not, now got to re-set up. To crown the other end again same applies, setup, crown, check concentric ( parallel ) to bore?. The final chambering can be done once the barrel is installed as well as the headspace checks. Reassemble function / feeding /extraction checks. Test fire, some will shoot for groups, some will just test fire for function. If anything is amiss it's back to the lathe.
Of course this is assuming that the action is not barreled or requires any truing or fixing / cleaning the gunk in the thread. Lapping of the lugs etc. I've pulled barrel from 1903's that was in place for almost 100 years, they can be quite challenging at times (I usually did this to reduce rebarrel cost /time before dropping of with the smith a time or two). 8 foot cheater bar, penetratingly oil, lots of heat some times (On the barrel not the action), or having to cut small relief in the barrel to get it to break lose. Then eventually rewarded with that loud crack noise which 75% of the time you swear you broke it.
There is way more involved in it than just chucking it in a lathe and go. Pre-fits, your action isn't even present, or a consideration. They have a pattern action to go by.
Time that this takes is not dependent on gunsmithing skills rather the gunsmith skills as a machinist. Fast turn around doesn't equate to job done correctly.
Which many times multiple other small repairs can be done time wise to one barrel installation. The smith's promise time and backlog will dictate what's on the bench. As well as $$ per day.
(in the case of large company it very well maybe a one man operation, as everyone else is making barrels.)
