I agree with Kutter on most points, but for the 1/2 rings, the scope is bore sighted while completely assembled, in order to establish the height of the rear ring. Once the rear ring is fit to the base, the scope is put back into the rings, lined up at the correct location and wired in position. Then witness marks are made with a scribe to allow returning the tube to the correct position after the scope is disassembled and prepped for soldering. During the soldering operation, the tube. rings, and barrel(d receiver) are all held together with wire and positioned IAW the witness marks.
It is easier to align the bases with screws as Kutter says, but if not closely fit, the bases are scrapped to achieve a "tight" joint. Where bases are not screwed, they are scrapped to fit and wired for soldering, aligned as closely as possible( using two pieces of key stock or similar), and then soldered. After the bases are soldered, a "skim" cut is made in a mill, to insure alignment between the bases( not done with screwed bases on bolt guns).
Then, everything is cleaned of solder residue, engraved( as appropriate) and blued. Scope tubes, and bolt guns are not typically rust blued because the solder joints are large enough to withstand the bluing salts( this also removes any solder residue missed in the polishing). Bases on soldered together barrel bundles are rust blued, because the rib joints may not withstand the salts.
Lastly, everything is reassembled and sighted in.
Mike