Here's some of the processes I've used, some require more $$ and effort. I've settled on the Easy button as mentioned. Occasionally I had a student that wanted to try some of old ways and used some of the recipes from R.H. Angier book, more often than not, lots of effort and mediocre results...
Damp cabinet, a bowl of nitric in the bottom, card and steam frequently, lots of work, lots of time.
The EASY button... Mark Lee's brown or bluing solution. A dozen of my students have used this on their builds, I've done several of my own with it, it really does do a quality job with a lot less hassle. Follow the instructions to the letter, no short cuts or getting lazy, or thinking you have a better idea, that's where most issues arise. If you have issues with it, go back and confirm your process, 90% of the time you've missed the mark -pun intended.
Simple household equipment - A boiler - I use a porcelain canning pot on a propane burner like the one used for the TG turkey. A piece of 3" PVC pipe with a cap, a box of the vintage Spic and Span (I prefer the stuff with TSP - I see Mark is recommending Simple Green now), always use distilled water, clean and dry your steel wool or Scotchbrite with acetone before you start. Some new clean cotton gloves (cleaned with the TSP solution and rinsed), and wire, also cleaned before using...
(You need to Login or Register to view media files and links) Small piece work, Brownells Nitre blue, again you'll need some equipment. It looks to be out of stock at Brownells.
(You need to Login or Register to view media files and links) If you want a very durable modern looking finish, Brownells oxynate no.7 hot caustic salts ( there are some hazard risks). You'll spend $$ on tanks and gear, you'll need a dedicated place to do it.
For blacking stainless, Brownells Oxynate no. 84. Similar equipment as the no.7 it's a hazardous material also but it works.
Been down all of these slopes, as mentioned for touch up - oxpho-blue. Don't try to do an entire rifle with this, it'll frustrate oneself.
I've used Pilkingtons rust blue, it's not a favorite as a damp cabinet gives the best results. There's quite a bit of effort that goes into it, but it will make barrels on doubles match the color of an action so in some places, it's required.
Hope this 5¢ worth of info helps...
GT