guns that are used and maintained develop a grey patina on the steel over the course of decades. Bluing and Browning are the same process, with one added step for bluing. Both are creating an oxidized layer.
Simple browning and bluing:
1. get the metal to the desired level of polish (the smoother it is, the more difficult it is to rust)
2. degrease the steel to be rusted
3. prepare a mix of water, Distiller's Vinegar, and salt (7:1:2 mix works), apply it to the steel
4. place the steel parts in plastic bags and place them in a warm place
5. reapply the mixture once a day until the steel is evenly rusted
6. card off the rust bloom (the loose, crumbly stuff on the very surface)
7. reapply the mixture and return it to the plastic
8. repeat the process several times
9. Card the final rusting until it's smooth
For browning, you stop here, and soak the steel in a thin oil for a bit, then dry it off and apply a heavy oil or wax (I like wax, you can buff it smooth and it holds up great)
For Bluing, you take your carded part and pour boiling water over it until the red iron oxide converts into black iron oxide, then soak the part in thin oil and coat in heavy oil/wax.
to reblue a part, you degrease it, rust it some more, and pour boiling water on it, that easy.
Or you can do what a lot of militaries did, and polish their pieces bright frequently, to prevent the patina from building up.
It's all personal preference, but I prefer Browned and blued steel, it doesn't shine as much, and that's nice for hunting. For a piece that just gets shot at the range or is a fowling piece, I don't mind the grey patina. Armory bright is too much work, IMO