A real Gunsmith must be able to take any gun, of any kind, fix any problem it may have including making replacement parts from scratch. Being a gunsmith also means you have to be a machinist, welder and a woodworker.
The Colorado School of Trades offers an in-house, hands on Gunsmith course. I hear its hard to get into due to a waiting list and if you do, it ain't cheap. Bear in mind that you will have to move there. This is a full time school.
The traditional method was to apprentice under a Master. But there are very few Masters left anymore and I seriously doubt one would take on a complete stranger.
I do all my own work. Learned mostly from books, videos and my own mistakes. I'm a pretty fair hobbyist, but no where near a real gunsmith.