I found this on google and thought I'd share my two cents.
I had a pretty good experience doing a correspondence/distance learning gun school, earning a diploma in the trade.
I went through 6 different 'instructions' which included everything from metallurgy, gun history, types of guns, etc. It was really a crash course in lot of info that I already knew but a lot that I thought I did but didn't really..
The problem with this kind of course is nothing beats hands on work with actual guns, but I already had a lot of that so I assume that once I get an apprenticeship or something like it I would be way ahead of the curve. I am kind of guessing that a lot of what I actually learned is a lot of technical stuff that even gunsmiths might not know offhand.
I would recommend doing this if you can't do a physical apprenticeship right off the bat, but it might be best to go the route of doing that if you can.
I didn't try to look for jobs yet but again, nothing beats a hands on training if you can get it. I know a lot more than I did though.
I found the gun course I took at http://www.smartschoolfinder.com/guide/gunsmithing-schools and I'm sure there are others out there. The name of the course I took was penn foster. Hope that helps.