Basically, the same way gunsmith's fit new sights.
After the sight is in place, the shank will protrude into the bore.
Using a Dremel tool and a fine stone, VERY carefully grind the shank down ALMOST flush with the bore.
Be careful to NOT actually mark the bore, so no slipping allowed.
After you've got it close, use a rubber polishing tip to take it the rest of the way.
After you've got it flush, either polish out the entire bore with steel wool on a rod to blend everything to a fine finish, or use finer polishing tips in the Dremel.
To polish the entire bore, use 0000 steel wool wrapped around a used bore brush, or make up a split dowel.
Chuck in a drill and run at medium speed, keeping the polishing head constantly moving.
In the old days before Dremel tools or Flex-shafts, gunsmith's wrapped fine sand cloth around a split wood dowel rod and either polished the protruding shank down by hand, or if they had it, a drill.