The two most certain methods are to go to an accredited gunsmith school like Trinidad State College, Colorado School of Trades, Lassen College, or one of the other good ones, then go to work for an established gunsmith.
The other is to serve an apprenticeship with an established gunsmith.
In both of these methods, you first learn about real-world gunsmithing, AND the business end of things. You also build up contacts, and a potential customer base.
It's possible to break in cold by getting a correspondence course, and just soliciting business, but this is TOUGH, and many people who attempt this route, "starve out" and fail as a business.
Another, somewhat over-rated method is the military armorer route. In this one, you join the military, and sign up to be taught to be a small arms armorer.
The problem with this is, most military armorers are actually gun REPAIRMEN. They learn how to get malfunctioning military weapons working again, by replacing parts. True military gunsmiths are actually rather rare, and in any case, are still experts on MILITARY weapons, not commercial sporting arms.
While it is possible to get going with correspondence courses, or even as a self-taught 'smith, the apprenticeship or school method have several big advantages:
1. You learn the actual, RIGHT method of doing things. If you're doing something wrong, or there's a better way to do it, an instructor is right there to point it out to you. No correspondence course can do this.
2. You get a wide range of experience, working on the school's guns. You're not learning by making mistakes on customer's guns, and you'll learn things you might go years without seeing.
3. You have an instructor who will do something the correspondent courses can't and won't do: Tell you that you that you just simply don't have the talent or skills necessary.
This is invaluable.
I attended a watchmaker's school when I was starting out in "the trades". There were a number of people who just weren't cut out to be watchmakers. They didn't have the talent, the temperament, or the ability to simply do the work.
Painful as it was to do, the instructors let them know that they should look at another career.
This can save a potential tradesman a bundle of money, time, and frustration. Nobody likes to be told they can't cut it, but a school or a working gunsmith will do the right thing for both you and the customer.
Once you've got the real skills of a gunsmith, there a many ways to get started in business, running from working for an established gunsmith, working for a large police department as a armorer, working for a gun company, or a "day job" and having a start-up gunsmithing business on the side.
As the business grows to the point where you are SURE you can make a living, you drop the other job, or continue to do both.