Hello Susie! Welcome to yorkie talk

I think it is great that you are interested in finding out what is typical protocol to ensure Yorkshire terriers are bred to be healthy, beautiful and well tempered dogs. Like Carolyn said, there are many tests that should be done to ensure that your dog is healthy and up to standard. We have some very knowledgable folks on here, I don't have their skill and knowledge at all! But a few things I would want to do is run a blood panel and get a bile acid test to check liver function (especially because liver issues can be prevelanr in yorkies) also, their knees should be checked to look for any degree of luxating patella.
Typically, the best path to having a high quality Yorkshire terrier whose type you would want to pass on is to go through the show route and do confirmation showing. Judges evaluate bite, gait, hair type and many other things and have a honed eye for what is desirable and represents the Yorkshire terrier breed according to their breed standard. That, coupled with many health evaluations seems like the way to start off. Find a local breed club, support the YTCA (Yorkshire terrier club of America) and start attending shows to learn what represents a good quality specimen of Yorkshire terrier. Perhaps your dedication will inspire an educated breeder to mentor you. I hope another more educated lady on the topic will Chime in with advice soon.