First of all welcome to you and Maggie. I am very new to the exhibitor/breeder world, so my ideas and opinions may differ from those with more experience. In fact, I have my first show bitch and am working very closely with two mentors to get her finished. It seems that the more I learn the more I realize how little I know. I hope I never stop learning - if I do, then it's time to find a new passion! Anyway...
The vast majority of exhibitor/breeders will not sell a dog or bitch to a person that they don't know and trust, so the first step would be to visit a lot of dog shows and get to know the exhibitor/breeders. Many are more than willing to "talk yorkie" after they have finished in the ring. After you get to know the exhibitor/breeders in your area and find someone that would be willing to mentor you. Work with your mentor, gain their trust, and then perhaps in time you can become a co-owner of a stud or bitch. Continue working closely with your mentor and finish your stud or bitch. While at shows, get a clear understanding of the standard and learn to spot faults. Start evaluating what YOU want to accomplish with your future breeding program and what you can do to improve the breed. The ultimate goal of a breeder should be to combine the genetics of a male and female and have the product of that breeding to be superior to the parents.
Of course between the acquiring a show prospect and breeding, there are the medical screenings and genetic testing. It can be very overwhelming to take on the tast of breeding to better the breed if you don't have a loyal and trusted mentor to help guide you.
Good luck, take your time and enjoy the journey!