How to become a breeder? Pretty easy if you go by my definition of what a breeder is.
How to become a QUALITY breeder (ie respectable breeder)... Well, I don't know about in chickens, but in other areas of my life I've worked for some of the best breeders, and now continue to breed.
So, my advice to a horse or dog "want-to-be-serious-breeder" is: read everything you can. Go to shows and network, meet as many people as you can, develop an eye for what you like. THEN sit down and figure out what your breeding goals are, just production? Trail? Show? Any breed or one breed? Etc. Try to start off with one breed, buy the best possible animal you can afford, and don't get attached. Then plan your breeding, see what comes out of it and go from there. In horses, I'd tell you start out with one mare, then slowly grow adding THE BESGT YOU CAN AFFORD! If you want to be serious about showing, and breeding to the standard, then you have to start out with the best you can, that may be better or worse than someone else's best...
Also, there will always be animals that don't make the grade, I usually sell them as trail horses as they are sound in mind and body, just not show quality, so have a plan for your culls/be prepared to cull, even the breeders if they aren't producing well enough.
And finally, "prove" that you're producing quality stock by going to shows or trail events, etc. and in about 3-5 years of consistent success (consistent being key) you can call yourself on the way to being a quality breeder, IMO.