The "browning" they describe is called "rust bluing" today.  It is the process of converting red iron rust (Fe₂O₃ to black iron oxide - Magnetite (Fe₃O₄)

It is actually pretty easy to do at home, and with a little practice, you can repair small spots on a larger piece without disturbing the original finish. 

It is far less hazardous than modern hot caustic bluing, and is far more durable.

The color from both color case hardening and nitre (fire) bluing is very delicate.  The only way I know to reliably protect it is to either not touch it, or to cover it in some sort of varnish.

I've attached a few pictures:
Picture 1:  Czech Vz52 rifle parts that I rust blued.
Picture 2:  Chilean Mauser screw that I nitre blued.
Picture 3:  Colors possible with nitre bluing.

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